;; ;; ;; ; ; emeronti cmnynkt; 0 emeronti tyeck nig BhuKuNrYm 08 emeronti tyeck nig BhuKuNrYm 6 emeronti TI4 RbPaK 7 emeronti5 cmnyntspak 8 emeronti6 PaKry 4 emeronti7 rgvas; ;rgval rgval; 46 emeronti8 kensambicknit 49 emeronti9 smikardwerktimyymanmyygbaøat 56 emeronti0 vismpab 7
emeronti lmhat;!>k-rkcmnynkt; n Edl 4 < n < 67. x-cmnynkt;ess a Edl 55 a < 65. @> KNnaRbmaNviFIénkenSamxageRkam ³ k> 40 5 50 6 7 60 x> ( 57 4 7 5) 0 4 90 K> 56 8 (47 7) 5 cmnynkt; X> [ 4 5 7 8 (47 ) 6] g> 75 8 75 5 7 8 9 7 5 6 7 #> enagnuvitüal½ymyymansissrbus ^&( nak; nig sissrsi %&*nak; kñúgmyyqñamsissedlganesovepaenakñúgbnñal½y)an $ k,al b ercincag $k,almancmnyn *@$ nak;. etisissedl)anganesovepaenakñúgbnñal½yticcag $ k,alman cmnynb:unµannak;? $> b unña)antijepøemon % cegáam EdlkñúgmYycegáam man!0 Epø. Kat;)anjaMGs; * Epø ehiyepøemonedlenasl;)anebgeck[b Ún² Kat; ^ nak;. etib ÚnKat;mñak;²TTYl)anemonb:unµanEpø? - -
emeronti cmnynkt; %> enakñúgfñak;eronmyymansissrbus!* nak; nig sissrsixøh. ebisissmñak;²ttyl)anesovetalmhat; @k,al ehiyesovepaedl )antijtamggs;mancmnyn &^ k,al. rkcmnynsissrsi? ^>bgát;cmnynxagerkamykrtwmxþg;db; xþg;ry nig xþg;ban; ³ k>!$((0% x> #*$000 K> @((0#$^ X> ^&%$%%0 &>efvikar):an;sµantémøén ³ k> 98 57 x> 648 999 K> 40 58 *> KNnatémøén k> 5 x> 5 K> 8 X> x ebi x 5 (>srmyl k> 9 6 x> 4 4 K> 96 5 64 00 X> 8 - -
emeronti cmnynkt; dmenahrsay!>k-rkcmnynkt; nedl 4 < n < 67 cmnynkt; n EdlenAcenøaH 4 nig 67 KW ³ 44,45,46,47,48, 49 50,5,5,5,54,55,56,57,58,59,60,6,6,6,64,65,66. x-cmnynkt;ess a Edl 55 a < 65 cmnynkt;ess a EdlenAcenøaH 55 nig 65 KW,57,59,6, 6 @> KNnaRbmaNviFIénkenSamxageRkam ³ k> 40 5 50 6 7 60 0 (4 5 5 6 7 6) 0 (0 0 4) 0 8 80 x> ( 57 4 7 5) 0 4 90 (00 5) 0 60 55. 65 0 60 00 60 660 K> 56 8 (47 7) 5 7 0 5 7 6 0 - -
emeronti cmnynkt; X> [ 4 5 7 8 (47 ) 6] [60 9 4 6] (69 4) 65 0 g> 75 8 75 5 7 8 9 7 5 6 7 75 9 5 7 7 9 7 5 4 75 9 05 5 4 4 4 09 #>cmnynsissedl)anganesovepaenakñúgbnñal½yticcag $ k,alman cmnyn ³ 679 578 84 4 nak;. $> b unña)antijepøemon % cegáam EdlkñúgmYycegáam man!0 Epø. Kat;)anjaMGs; * Epø ehiyepøemonedlenasl;)anebgeck[b Ún² Kat; ^ nak;. etib ÚnKat;mñak;²TTYl)anemonb:unµanEpø? -cmnynepøemonsrub ³ 5 0 50Epø -cmnynepøemonenasl; ³ 50 8 4 Epø -cmnynepøemonedlb Ún²TTYl)an ³ 4 6 7Epø. - 4 -
emeronti cmnynkt; %> enakñúgfñak;eronmyymansissrbus!* nak; nig sissrsixøh. ebisissmñak;²ttyl)anesovepalmhat; @k,al ehiyesovepaedl )antijtamggs;mancmnyn &^ k,al. rkcmnynsissrsi? -cmnynsissrsi ³ 76 8 8 8 0 nak; ^>bgát;cmnynxagerkamykrtwmxþg;db; xþg;ry nig xþg;ban; ³ k>!$((0% -ykrtwmxþg;db;kw: ³ 49905 4990 -ykrtwmxþg;rykw ³ 49905 49900 -ykrtwmxþg;ban;kw ³ 49905 50000 x> #*$000 -ykrtwmxþg;db;kw: ³ 84000 84000 -ykrtwmxþg;rykw ³ 84000 84000 -ykrtwmxþg;ban;kw ³ 84000 84000 K> @((0#$^ -ykrtwmxþg;db;kw: ³ 99046 99050 -ykrtwmxþg;rykw ³ 99046 990400-5 -
emeronti cmnynkt; -ykrtwmxþg;ban;kw ³ 99046 990000 X> ^&%$%%0 -ykrtwmxþg;db;kw: ³ 6754550 6754550 -ykrtwmxþg;rykw ³ 6754550 6754600 -ykrtwmxþg;ban;kw ³ 6754550 6755000 &>efvikar):an;sµantémøén ³ k> 98 57 400 500 900 x> 648 999 4000 000 5000 K> 40 58 400 60 70 *> KNnatémøén k> 5 4 5 5 00 5 500 x> 5 5 9 4 K> 8 64 9 55 X> x ebi x 5 ek)an x 5 5 75 (>srmyl k> 9 6 4-6 -
emeronti cmnynkt; x> 4 4 6 4 K> 00 96 0 4 40 X> 5 64 8 5 4 7 7 7-7 -
emeronti lmhat;!>curbba ak;fa ³ k> plbuk 78 0 Eckdac;nwg x> pldk 440 70 Eckdac;nwg K> plbuk 65 70 Eckdac;nwg 5 tyeck nig BhuKuN X> pldk 50 4 Eckdac;nwg 9 @> ekmanmyycmnynmanelxr)amxþg; 74 0 bmebjelxkñúgrbgb;edim,i[cmnynenaheckdac; ³ k> nwg pg nig 5 pg x> nwg pg nig 9 pg. #> ekmancmnyn 660, 540, 645 nig 60. eticmnynnaxøhcabhukunén 0? $> ekmancmnyn, 5, 7, 8, 9, 0,,, nig9 k>currktyeckéncmnynnimyy² x>eticmnynnaxøhcacmnynbfm %> bmebkcmnyn 6, 00,9, 5, 567, 980, 097, 506 nig 7008 CaplKuNktþabfm. - 8 -
emeronti ^>rktyeckrymfmbmput PGCD éncmnynxagerkam ³ k> 9 nig 5 x> 0 nig 08 K> 8 nig 4 X> 9, 60 nig 96 g>, 7 tyeck nig BhuKuN 48 nig c>, 68, 44 &>rkbhukunrymtucbmput ( PPCM b ) k> 8 nig 5 x> 0 nig 5 K>, 40 6 nig 5 LCM éncmnynxagerkam ³ 4 nig 45 X> 70, nig 8 g>, 8 5 nig 0 c>, 0 *> rkcmnyn x nig y edaydwgfa (x, y) y Edl 0 < x < y. (>rkcmnyn x EdltUcCageKbMputedaydwgfa PPCM (6, x) 4 88 nig 58 PGCD nig x 7-9 -
emeronti dmenahrsay!>curbba ak;fa ³ k> plbuk 78 0 Eckdac;nwg ekman 78 0 98 cugerkaycacmnynku. tyeck nig BhuKuN Eckdac;nwg erbahcmnynenhmanelx x> pldk 440 70 Eckdac;nwg ekman 440 70 40 elxlmdab; 4 0 9 Eckdac;nwg. Eckdac;nwg erbahplbuk K> plbuk 65 70 Eckdac;nwg 5 ekman 65 70 45 edayelx 5. Eckdac;nwg 5 erbahelxcugerkaybba b; X> pldk 50 4 Eckdac;nwg 9 ekman 50 4 4788 Eckdac;nwg 9 erbahplbukelx lmdab; 4 7 8 8 7 Eckdac;nwg 9. - 0 -
emeronti tyeck nig BhuKuN @> ekmanmyycmnynmanelxr)amxþg; 74 0 bmebjelxkñúgrbgb;edim,i[cmnynenaheckdac; ³ k> nwg pg nig 5 pg edaycmnynenhmanelxcugerkaycaelx 0 enahvaeckdac;nwg ehiynwg 5 Canic. ducenhelxedlrtuvbmebjkñúgrbgb;enahkw ³ 0,,,,4,5,6,7,8,9. x> nwg pg nig 9 pg. edayplbukelxlmdab; 7 4 0 4 edim,i[cmnyn 74 0 Eckdac;nwg pg nig 9 pgluhrtaet vaeckdac;nwg 9. ducenhelxedlrtuvbmebjkw 4. #> ekmancmnyn 660, 540, 645 nig 60. eticmnynnaxøhcabhukunén 0? cmnynedlcabhukunén 0 KW 660, 540. $> ekmancmnyn, 5, 7, 8, 9, 0,,, nig9 k>currktyeckéncmnynnimyy² -cmnyn mantyeck nig -cmnyn 5 mantyeck,, 5 nig 5 - -
emeronti tyeck nig BhuKuN -cmnyn 7 mantyeck nig 7 -cmnyn 8 mantyeck,, 6, 9 nig 8 -cmnyn 9 mantyeck nig 9 -cmnyn 0 mantyeck,, 4,5, 0 nig 0 -cmnyn mantyeck,, 7 nig -cmnyn mantyeck,, nig -cmnyn 9 mantyeck nig 9 x>eticmnynnaxøhcacmnynbfm %> bmebkcmnyn 6, 00,9, 5, 567, 980, 097, 506 nig 7008 CaplKuNktþabfm. 6 00 9 9 5 567 980 097 7 4 5 5 7 9 5 - -
emeronti tyeck nig BhuKuN 506 5 7008 4 5 4 7 ^>rktyeckrymfmbmput PGCD éncmnynxagerkam ³ k> 9 nig 5 PGCD (9,5 ) x> 0 nig 08 PGCD (0,08) K> 8 nig 4 PGCD (8, 4 ) X> 9, 60 nig 96 4 PGCD (9,60,96 ) g> 48, 7 nig PGCD (48,7, ) c> 6, 68, 44 nig 5 PGCD (6,68,44, 5 ) - -
emeronti tyeck nig BhuKuN &>rkbhukunrymtucbmput ( PPCM b LCM ) éncmnynxagerkam ³ k> 8 nig 5 PPCM (8, 5) x> 0 nig 5 05 PPCM (0, 5) K> 4, 40 nig 45 840 PPCM (4,40, 45) X> 70, nig 8 PPCM (70,, 8 ) g> 5, 8 nig 0 40 940 PPCM (5,8, 0 ) c> 88, 0 nig 58 940 PPCM (88, 0,58) 640 *> rkcmnyn x nig y edaydwgfa (x, y) Edl 0 < x < y. eday PGCD (x, y) enah x p, y q Edl (p,q) PGCD. PGCD nig x y 7-4 -
emeronti tyeck nig BhuKuN ekman x y 7 ek)an p q 7 b p q 6 eday 0 < x < y enah 0 < p < q ektaj p, q 5 ducenh x, y 60. (>rkcmnyn x EdltUcCageKbMputedaydwgfa PPCM (6, x) 4 eday 4 6 4. ducenh x 4 CatémøtUcCageKEdl PPCM (6, x) 4. - 5 -
emeronti cmnynkt;rwlatihv lmhat;!>sresrcmnynkt;rwulatib 7,5, 0,0,,,8,,9,, 4,. k>tamlmdab;elig x>tamlmdab;cuh @> edacmnuc A( 4),B( 6),C() nig D (5) elibnþat;cmnyn rycknna RbEvg AB, AC nig BC. #> bmebjsmpabxagerkam ³ k> 4... x>... K> a 7 nig b CacMnYnpÞúyén a enah b... $> KNnaplbUkxageRkamedayeRbIbnÞat;cMnYn ³ k> 4 6 x> 5 ( ) K> 7 ( ) X> 0 5 g> ( 4) %> bmebjsmpabxagerkam ³ k> 9... 0 x> 5... K> 8... X> 5... 8 g> 6 5... c> 7 ( )... - 6 -
emeronti ^>KNnapldk ENnaM ³ 0 6 0 ( 6) k> 7 4 x> 7 K> 0 g> ( 0) cmnynkt;rwlatihv b 5 ( 9) 5 (9) X> 0 ( 5) c> 5 q> ( ) &>KNnakenSamxageRkam ³ k> 0 ( 7) x> 4 ( 6) K> 7 ( 6) 4 X> 8 ( ) g> 4 6 ( 5) c> 5 ( 8) *> KNnarYceRbobeFob k> 0 nig 0 x> ( 9) ( 5) nig ( 5) ( 9) etivifidkmanlkçn³rtlb;b et? K> [ 4 ( 7)] nig 4 [( 7) ] X> ( 7) nig (7 ) etivifidkmanlkçn³pþmúb et? - 7 -
emeronti (>KNnaplKuNxageRkam ³ k> ( 6)( 4) cmnynkt;rwlatihv x> ( )( ) K> 9)(7) ( X> ( 0)( 9) g> ( 500)( 0) q> (59)!0> bmebjcenøahkñúgsmpabxagerkam ³ c> ( 5)(400) k> 5 ( )(...) x> ( )(...) K> 4 ( )(...) X> ( 0)(...) 4 g> (...)( ) 78 c> ( )(...) q> ( 7)(...) 0!!> KNnaplEckxageRkam ³ k> ( 6) 9 C> (...)( 5) 0 x> 50 ( 5) K> ( 45) 9 44 g> q> X> c> ( 7 0) C> 9 40 5 [ ( 8)] [ 5 ( 5)] 0-8 -
emeronti cmnynkt;rwlatihv!@> KNna k> 6 9 ( ) x> 0 8 K> 6 9 5 X> 4 g> 7 ( 5) c> 8 q> [5 ( )] C> 50 [5 ( )] Q> 80 0 7!#> KNnakenSamelxxageRkam ³ k> 8 [7 ( 5)] x> [ 40 ( )] 6 K> [( 5) 7] ( 8 7) X> [ 5700 4(88 )] (8 ) g> 00 {[50 (40 8)] [ 7 (9)]}!$> bunamanxøi % RKab; bgkat;[xøiefm # RKab;eTot. buna)an elgxøicamyysmcaj;gs;xøi!0rkab;. etibunartuvcmbak;xøismcmnynb:unµanrkab;? - 9 -
emeronti cmnynkt;rwlatihv dmenahrsay!>sresrcmnynkt;rwulatib 7,5, 0,0,,,8,,9,, 4,. k>tamlmdab;elig,, 0, 7,,0,,,5,8,9,,4. x>tamlmdab;cuh 4,,9,8,5,,,0,, 7,,,. @> edacmnuc A( 4),B( 6),C() nig D (5) elibnþat;cmnyn rycknna RbEvg AB, AC nig BC. ek)an AB 4 ( 6) 4 6 AC ( 4) 4 7 BC ( 6) 6 9-0 -
emeronti cmnynkt;rwlatihv #> bmebjsmpabxagerkam ³ k> 4 4 x> K> a 7 nig b CacMnYnpÞúyén a enah b 7 7 %> bmebjsmpabxagerkam ³ k> 9 ( 9) 0 x> 5 ( ) K> 8 ( 4) X> 5 ( ) 8 g> 6 5 ( ) c> 7 ( ) ( ). ^>KNnapldk ENnaM ³ 0 6 0 ( 6) k> 7 4 x> 7 5 K> 0 X> 0 ( 5) 5 b 5 ( 9) 5 (9) - -
emeronti cmnynkt;rwlatihv g> ( 0) c> 5 8 q> ( ) 6 &>KNnakenSamxageRkam ³ k> 0 ( 7) 0 7 7 5 x> 4 ( 6) 4 6 4 8 4 K> 7 ( 6) 4 7 6 4 7 0 7 X> 8 ( ) 8 8 5 g> 4 6 ( 5) 4 6 5 5 c> 5 ( 8) 5 8 - -
emeronti *> KNnarYceRbobeFob k> 0 7 nig 0 7 ducenh 0 ( 0) x> ( 9) ( 5) 9 5 4 nig ( 5) ( 9) 5 9 4 ducenh ( 9) ( 5) [( 5) ( 9)] vifidkkµanlkçn³rtlb;et. K> [ 4 ( 7)] 4 7 9 nig 4 [( 7) ] 4 ( 7 ) 4 7 ducenh [ 4 ( 7)] 4 [( 7) ] X> ( 7) 7 0 nig (7 ) 4 8 ducenh ( 7) (7 ) vifidkkµanlkçn³pþmúet. (>KNnaplKuNxageRkam ³ cmnynkt;rwlatihv k> ( 6)( 4) 4 x> ( )( ) 6 - -
emeronti cmnynkt;rwlatihv K> ( 9)(7) 6 X> ( 0)( 9) 90 g> ( 500)( 0) 5000 c> ( 5)(400) 6000 q> (59) 89!0> bmebjcenøahkñúgsmpabxagerkam ³ k> 5 ( )(5) x> ( )() K> 4 ( )(4) X> ( 0)(...) 4 mingacman g> ( 6)() 78 c> ( )(4) q> ( 7)(0) 0 C> ( 6)( 5) 0!!> KNnaplEckxageRkam ³ k> ( 6) 9 x> 50 ( 5) - 4 -
emeronti cmnynkt;rwlatihv K> ( 45) 9 5 40 X> 8 5 44 g> 4 [ ( 8)] c> ( 7 0) q> 9 [ 5 ( 5)] C> 0!@> KNna k> 6 9 ( ) 5 x> 0 8 8 6 K> 6 9 5 6 4 X> 4 48 44 g> 7 ( 5) 7 ( 0) 70 c> 8 6 q> [5 ( )] ( 0) 0 C> 50 [5 ( )] 50 ( 0) 5 Q> 80 0 7 4 7-5 -
emeronti!#> KNnakenSamelxxageRkam ³ k> 8 [7 ( 5)] cmnynkt;rwlatihv 8 4 x> [ 40 ( )] 6 ( 40 ) 6 40 8 K> [( 5) 7] ( 8 7) ( 46 7) ( 7) 84 X> [ 5700 4(88 )] (8 ) (5700 400) 6 400 6 700 6 50 g> 00 {[50 (40 8)] [ 7 (9)]} 00 [55 ( 6)] 00 ( 480) 5 4!$> bunamanxøi % RKab; bgkat;[xøiefm # RKab;eTot. buna)an elgxøicamyysmcaj;gs;xøi!0rkab;. etibunartuvcmbak;xøismcmnynb:unµanrkab;? cmnynxøiedlbunacmbak;sm KW. erbah 5 0-6 -
emeronti4 lmhat;!>bmebjcmnynkñúgrbgb;xagerkam ³ (...) k> 5 0 (...) 4 K> x> 4 8 (...) (...) @> srmylrbpakxagerkam ³ 6 k> 9 8 x> X> 84 K> 96 g> 4464 #> KNna x nig y xagerkam ³ 6 k> (...) 8 8 65 000 x 5 0 x> 7 y 8 8 x. X> x 7 K> $> erbobefob nig erobryrbpakxagerkamtamlmdab;cuh k> 7 5 4,,, x> 7 7,,,, 6 9 4 8 RbPaK - 7 -
emeronti4 %> bmebjsbaøa (, > ) < kñúgrbgb;xagerkam ³ 8 7 k> 9 9 x> 6 0 K> 7 7 X> ^>KNnarYcsRmYl 4 7 k> x> 0 0 7 8 K> 5 5 8 7 g> c> 5 5 5 4 q> 4 5 8 C> &>KNnarYcsRmYllTæpl 4 k> K> g> q> X> 7 4 6.. 8 8 4 4 5.. 0 8 9 6. 8 7 6 7 0 x> 5 4 7 5 4 X> ( 8. ) (. ) 9 8 8 9 5 9 6 c> 8 7 4. 4 4 RbPaK - 8 -
emeronti4 RbPaK *> KNnarYcsRmYl k> x> 7 5 8 K>.. 5 4 6 4 X> (.. ) ( ) 6 5 4 0 g> 7 7 5 5 5 c> q> 5 5 4 6 4 5 5 (>BinitülMnaMKMrU 7 6 8 4 0, tamlmnamkmruenhcurknna ³ 4, 4 7 7 4... 4 5 995 996-9 -
emeronti4 RbPaK - 0 -!0> BinitülMnaMKMrU ³ 5 4 4, 5,, sresrrbpak 7, 6, 5 nig 8 tamlmnamkmruxageli?
emeronti4 dmenahrsay!>bmebjcmnynkñúgrbgb;xagerkam ³ k> 5 0 7 8 x> 8 6 4 K> 4 8 8 @> srmylrbpakxagerkam ³ 6 k> 9 8 6 x> 84 K> 96 7 65 5 X> 000 8 g> 4464 #> KNna x nig y xagerkam ³ x 6 k> 7 7 6 ek)an x. RbPaK - -
emeronti4 RbPaK x> 5 0 y 8 5 8 y. ek)an 7 0 K> x. 7 7 4 ek)an x 9 8 X> x 8 8 ek)an x. $> erbobefob nig erobryrbpakxagerkamtamlmdab;cuh 7 5 4 k>,,, 6 9 4 7 5 ek)an < < < 9 6 7 nig erobryrbpakxagerkamtamlmdab;cuh,,, 6 7 7 x>,,,, 4 8 7 7 ek)an < < < < 4 8 7 nig erobryrbpakxagerkamtamlmdab;cuh,,, 5 4. 9 7,. 8 4 - -
emeronti4 %> bmebjsbaøa (, > ) < kñúgrbgb;xagerkam ³ 8 7 k> < 9 9 x> > 6 0 K> > 7 7 X> < ^>KNnarYcsRmYl k> x> K> X> g> c> q> C> 4 7 4 7 0 0 0 0 7 4 (48 7) (4 4) 55 8 7 6 8 8 8 8 8 7 8 7 8 5 5 5 5 5 5 8 7 8 0 4 6 7 4 4 8 7 8 7 6 RbPaK 5 5 5 5 5 4 4 5 58 5 9 58 5 5 5 0 8 0 8 0 8 90 767 90 4 4 4 6 0 6 5 8 5 9 45 45 9 6 6 8 7 6 8 7 6 88 4 6 88 7 7 - -
emeronti4 &>KNnarYcsRmYllTæpl 4 80 k> 0 6 5 5 7 7 ( ) () x> 4 7 4 7 4 5 4 ( 5) ( ) (4) 9 8 8 9 9 8 9 5 X> ( 8 ) ( ) 0 5 5 9 6 9 7 g> 8 7 8 6 8 4 49 c> ( ) 4 4 4 8 K> 0 q> 4 *> KNnarYcsRmYl 9 4 4 7 6 k> 5 8 ( ) 0 x> 7 8 5 RbPaK - 4 -
emeronti4 RbPaK K> 5 4 6 4 5 7 5 5 4 4 X> ( ) ( ) 6 5 4 0 7 5 8 5 5 6 5 4 0 4 5 4 4 4 5 5 g> 7 7 5 5 5 6 7 7 6 5 5 5 5 5 50 86 c> 5 4 5 4 5 5 6 4 8 6 4 5 6 7 4 0 5 7 4 8-5 -
emeronti4 RbPaK - 6 - q> 7 7 0 8 4 6 7 6 8 5 9 8 5 7 8 7 6 5 9 4 6 5 (>BinitülMnaMKMrU 4 4,, tamlmnamkmruenhcurknna ³ 996 995... 5 4 4 996 995 996 ) 996 995 (... ) 5 4 ( ) 4 ( ) ( ) (!0> BinitülMnaMKMrU ³ 7 5 4 4, 5,, sresrrbpak 7, 6, 5 nig 8 tamlmnamkmruxageli
emeronti4 RbPaK - 7 - ek)an 9 7 5 5 5 5 9 7 5 8 8 9 7 5 7 7 9 7 5 6 6
emeronti5 lmhat;!>sresrrbpaknimyy²xagerkamcacmnyntspak ³ 7 k> 0 x> 00 59 K> 000 X> 45 0000 cmnyntspak g> 5 @> sresrcmnyntspaknimyy²xagerkamcarbpakcrmuh CaTRmg;Edl brgym)an ³ k>. 8 0 x> 0. 065 K>. 75 8 X> 0. 48 g> 8. 7 #> KNnatémøxageRkam ³ k>.48 6. 94 x> 4.765 85. 89 K> 0.096 7.67 0. 598 X>.64 7. 86 g>. 8. 56 5.8 0.7 9.6 4 c> ( ) ( ) - 8 -
emeronti5 $> rktémøxagerkam ³ k> 4.7 x>.4 8 0. 059 cmnyntspak K> 4. ( 0.8) (.4) X> [ 5.9 ( ) ] 5 g> 9. [( 4.) 0.7]. 6 c> 0. [ 99 ( 00) ] ( 0.005) q> ( 4 0.7) (0.06.) 4 %> KNnatémøxageRkam ³ k>.8 4 0 x>.4 6 K> (.7) ( 0.5) X> g> 0.8 [.54 (.8)] 0. 00 8 4.6 ^>BIraCFanIPñMeBjeTAextþeBaFisat;mancm ay.65km extþkmbugqñamgsßitenacenøahpñmebj nig extþebafisat;. ebikmbugqñamgmancm ay 9.45km BIPñMeBj. etibiextþkmbg;qñamgetaextþebafisat;mancm ayb:unµan km? 89. - 9 -
emeronti5 dmenahrsay!>sresrrbpaknimyy²xagerkamcacmnyntspak ³ 7 k> 0. 7 0 x> 0. 00 59 K> 0. 059 000 45 X> 0. 45 0000 g> 0. 5 5 4 cmnyntspak @> sresrcmnyntspaknimyy²xagerkamcarbpakcrmuh CaTRmg;Edl brgym)an ³ 8 4 k> 0.8 0 5 65 x> 0.065 000 00 875 67 K> 8.75 000 8 48 X> 0.48 000 5 g> 8.7 87 0-40 -
emeronti5 cmnyntspak #> KNnatémøxageRkam ³ k>.48 6.94 8. 5 x> 4.765 85.89. 655 K> 0.096 7.67 0.598. 64 X>.64 7.86 4. 454 g> 4. 8.56 5. 74 c> 5.8 ( 0.7) ( 9.6) 5.8 0.7 9.6 5.4 $> rktémøxagerkam ³ k> 4.7 55. 5 x>.4 8 0.059. 8 K> 4. ( 0.8) (.4) 5. 4 X> [ 5.9 ( ) ]. 56 5 g> 9. [( 4.) 0.7].6 46. 78 c> 0. [ 99 ( 00) ] ( 0.005). q> ( 4 0.7) (0.06.) 0. 9766 4-4 -
emeronti5 cmnyntspak %> KNnatémøxageRkam ³ k> 0.8 4 0. x>.4 6 0. 568 K> (.7) ( 0.5). 54 8 4.6 X> 4.6. 75 8 g> 0.8 [.54 (.8)] 0. 00 0.8 ( 0.6)(0.00) [ ] 0.8 ( 0.000) 500 ^>BIraCFanIPñMeBjeTAextþeBaFisat;mancm ay.65km extþkmbugqñamgsßitenacenøahpñmebj nig extþebafisat;. ebikmbg;qñamgmancm ay 9.45km BIPñMeBj. etibiextþkmbg;qñamgetaextþebafisat;mancm ayb:unµan km? 89. ek)an ³ 89.65km 9.45km 98.0km ducenhbiextþkmbg;qñamgetaextþebafisat;mancm ay 98.0km. - 4 -
emeronti6 lmhat;!>sresrpakrynimyy²carbpak nig CacMnYnTsPaK ³ k> 48 % x> 8 % K> 7.5% X> 66 % g> 99 % c> 0 % @> bþúrrbpak nig cmnyntspaknimyy²capakry ³ k> 7 6 x> 0 X>. 095 0 g>. 5 7 K> 0. 78 c> 6 5 PaKry #> Rkumh unmyy)ankat;bnßybukálikcmnyn 4 nak;ecjbibukálik 400 nak;. etibukálikedl)ankat;bnßymanb:unµanpakry? $> enamnðle)aheqñatmyykenøgmangñkcuheqµahe)aheqñat 8500nak; ehiyenaéf e)aheqñatman 5% éngñkcuheqµahmin)anmke)aheqñat. KNnacMnYnmnusSEdl)anmke)aHeqñat? %> BUsM)anepJIR)ak; 0000000erolenAFnaKarmYyedayTTYl)an GRtakarR)ak; 7 %. etiryheblb:unµanetibkat;ttyl)anr)ak; TaMgedImTaMgkar)an 95000 erol? - 4 -
emeronti6 dmenahrsay!>sresrpakrynimyy²carbpak nig CacMnYnTsPaK ³ 48 k> 48 % 0. 48 00 5 8 7 x> 8 % 0. 8 00 5 75 K> 7.5% 0. 75 000 8 66 X> 66 % 0. 66 00 50 99 g> 99 % 0. 99 00 0 c> 0 %. 0 00 0 @> bþúrrbpak nig cmnyntspaknimyy²capakry ³ 6 k> 85.7% 7 7 x> 85% 0 K> 0.78 78% X> 0.095 0.95% g>.5.5% 6 c> 4% 5 5 PaKry - 44 -
emeronti6 PaKry #> Rkumh unmyy)ankat;bnßybukálikcmnyn 4 nak;ecjbibukálik 400 nak;. etibukálikedl)ankat;bnßymanb:unµanpakry? 4 bukálikedl)ankat;bnßyman ³ 0.06 6% 400 $> enamnðle)aheqñatmyykenøgmangñkcuheqµahe)aheqñat 8500nak; ehiyenaéf e)aheqñatman 5% éngñkcuheqµahmin)anmke)aheqñat. KNnacMnYnmnusSEdl)anmke)aHeqñat? KNnacMnYnmnusSEdl)anmke)aHeqñat ³ 8500 8500 5% 8500 95% 8075nak;. %> BUsM)anepJIR)ak; 0000000erolenAFnaKarmYyedayTTYl)an GRtakarR)ak; 7 %. etiryheblb:unµanetibkat;ttyl)anr)ak; TaMgedImTaMgkar)an 95000 erol? 95000 ryhebledlkat;epji ³ 5. 66. 0000000 7% - 45 -
emeronti7 rgvas;rgval; lmhat;!>buplefvim úledrmyyedimmanrbevg 5 cm. k> ebikat;manedkrbevg 460mm etikat;efivm úl)anb:unµanedim? x> ebi 0% énedkrtuvxateblefvi etikat;efivm úl)anb:unµanedim? @> lkçikavas;kmnat;)anmyypab;edayerbiem:rteqimanrbevg 98 cm rycnagvas;pab;dedledayerbiem:rtsmbt;edlmanrbevg 99 cm kñúgkarvas;elikerkayenhnagexijfapab;kmnat;xøicagmun cm. etikmnat;bitr)akdmanrbevgb:unµanem:rt? #> mnussebjv½ymñak;manqam 5. 5 lit. ebiekdwgfaqam mm manekalikarkhm % lan. rkcmnynekalikarrkhmtamggs;? $> rfynþmyysiusamggs; 9 lit kñúg 00 km. ebifugsamgrfynþmanragrbelbieb:tekgedlmanvimart ³ 85 cm, 45cm, cm edayvas;bixagerka. ebicmnuh 0 % ticcagmadedl)anknnatamrubmnþ. k> etifugsamgrfynþenahmancmnuhbitb:unµanlit? x>etirfynþenahgacefvidmeni)anb:unµankilúem:rt? - 46 -
emeronti7 rgvas;rgval; dmenahrsay!>buplefvim úledrmyyedimmanrbevg 5 cm. k> ebikat;manedkrbevg 460mm etikat;efivm úl)anb:unµanedim? x> ebi 0% énedkrtuvxateblefvi etikat;efivm úl)anb:unµanedim? cemøiy k> cmnynm úledlkat;efiv)an eday 460 mm 46cm nigm úledrmyyedimmanrbevg 5 cm 46 ducenh edim 5 x> ebi 0% énedkrtuvxateblefvi enahkat;efivm úl)ankw ³ 46 46 0% 46 80% 0 edim 5 5 #> mnussebjv½ymñak;manqam 5. 5 lit. ebiekdwgfaqam mm manekalikarkhm % lan. rkcmnynekalikarrkhmtamggs;? edayqam 5. 5lIt 5.5dm 5500 000mm ducenhcmnynekalikarqamtamggs;man ³ 5500000 5lan 7 500000 lan. - 47 -
emeronti7 rgvas;rgval; $> rfynþmyysiusamggs; 9 lit kñúg 00 km. ebifugsamgrfynþmanragrbelbieb:tekgedlmanvimart ³ 85 cm, 45cm, cm edayvas;bixagerka. ebicmnuh 0 % ticcagmadedl)anknnatamrubmnþ. k> etifugsamgrfynþenahmancmnuhbitb:unµanlit? x>etirfynþenahgacefvidmeni)anb:unµankilúem:rt? cemøiy k> cmnuhbitkitcaliténfugsamgrfynþ ³ -madrbs;fugsamg ³ 85 45 45900cm 45. 9 lit ebicmnuh 0 % ticcagmadedl)anknnatamrubmnþducenhcmnuhbit KitCalIténFugsaMgKW 45.9 90% 4. lit. x>cm ayedlrfynþenahgacefvidmenir)an ³ 4. 00km 459km. 9-48 -
emeronti8 kensambicknit lmhat;!>sresrcakensambicknittaml,hxagerkam ³ k> byndk x x> y buk 0 K> kaerénplbuk x nig y X> b buknwgplkunmnign g>plkunrvag x buk y nig x dk y. @> k> plbukénbircmnynesµinwg 80. ebicmnyntimyyesµinwg x. cursresrkensambicknitsrmab;cmnyntibir? x> pldkénbircmnynesµinwg 0 ebicmnynedltuccagektagedayy sresrcakensambicknitsrmab;cmnynmyyetot? #> KNnatémøkenSamBICKNit x (y ) cmebah ³ k> x 7 nig y x> x nig y K> x 5 nig y 4 $> rfynþmyymanel,ónmfüm 60 km / h. sresrrubmnþcm aycr d kñúgryhebl t rycknnacm aycr kalnaekebikbrkñúgryhebl nig h5mn t. t h, t h0mn,t 0mn - 49 -
emeronti8 kensambicknit %> ctuekanekgmyymanbenþayesµinwg 5 m nig TTwg x m. k> sresrrubmnþbrimart P énctuekanekg? x> KNnabrimaRtctuekaNEkgcMeBaH x 5m, x 8m, x 0m ^> KNna k> x 7x x> x 5x K> x 6x X> 4x ( 8x) &> BnøatkenSam ³ k> ( x )(x ) x> ( x )(x ) K> ( x )(5 x) X> ( x )(x ) g> ( x )(y ) c> 4 (x ) (x 5)(x ) q> ( x) (x )(x ) *> dak;caplkunktþa ³ k> ax bx x> ax ab K> a ab X> 5x 0x g> a b c c> 8x y 4z q> (x 4) x(x 4) C> ( x 5)(x ) (x )(x 5) Q> xy x 4y j> ab 7b ac 7c - 50 -
emeronti8 dmenahrsay!>sresrcakensambicknittaml,hxagerkam ³ k> byndk x sresr 4 x x> y buk 0 sresr y 0 K> kaerénplbuk x nig y sresr ( x y) kensambicknit X> b buknwgplkunm nign sresr b mn g>plkunrvag x buk y nig x dk y sresr ( x y)(x y) @> k> plbukénbircmnynesµinwg 80. ebicmnyntimyyesµinwg x. cursresrkensambicknitsrmab;cmnyntibir? x> pldkénbircmnynesµinwg 0 ebicmnynedltuccagektagedayy sresrcakensambicknitsrmab;cmnynmyyetot? cemøiy k> sresrkensambicknitsrmab;cmnyntibir tag y CacMnYnTIBIr ek)an x y 80 ducenh y 80 x. x> sresrcakensambicknitsrmab;cmnynmyyetotkw y 0. - 5 -
emeronti8 kensambicknit #> KNnatémøkenSamBICKNit x (y ) cmebah ³ k> x 7 nig y ek)an x (y ) 7(6 ) 7 8 56 x> x nig y ek)an x (y ) ( )( ) K> x 5 nig y 4 ek)an x(y ) (5)( ) 50 $> rfynþmyymanel,ónmfüm 60 km / h. sresrrubmnþcm aycr d kñúgryhebl t rycknnacm aycr kalnaekebikbrkñúgryhebl t h, t h0mn,t 0mn nig t h5mn. cemøiy sresrrubmnþcm aycr d kñúgryhebl t KW d 60t -ebi t h enah d 60 0km. 0 7 7 -ebi t h0mn h enah d 60 40km 60 -ebi t 0mn h enah d 60 0km. - 5 -
emeronti8 kensambicknit %> ctuekanekgmyymanbenþayesµinwg 5 m nig TTwg x m. k> sresrrubmnþbrimart P énctuekanekg? x> KNnabrimaRtctuekaNEkgcMeBaH x 5m, x 8m, x 0m cemøiy k> sresrrubmnþbrimart P énctuekanekg ek)an P (5 x) 0 x x> KNnabrimaRtctuekaNEkgcMeBaH x 5m, x 8m, x 0m -ebi x 5m enah P 0 5 40m -ebi x 8m enah P 0 8 46m -ebi x 0m enah P 0 0 50m ^> KNna k> x 7x 0x x> x 5x x K> x 6x 8x X> 4x ( 8x) x &> BnøatkenSam ³ k> (x )(x ) x x x x - 5 -
emeronti8 kensambicknit x> (x )(x ) x x x 6 x x 6 K> (x )(5 x) 0x 6x 5 9x 6x 9x 5 X> (x )(x ) x x x 9 x 6x 9 g> ( x )(y ) xy 4x y 6 c> 4 (x ) (x 5)(x ) 4x x x 7 x 5x 5 q> ( x) (x )(x ) 4 x x x 5x 6 x 6x *> dak;caplkunktþa ³ k> ax bx x(a b) x> ax ab a(x b) K> ab a a(b ) X> 5x 0x 5x(x ) g> a b c (a b c) c> 8x y 4z 4(x y z) q> (x 4) x(x 4) (x 4)( x) - 54 -
emeronti8 kensambicknit C> ( x 5)(x ) (x )(x 5) (x 5)(x x ) (x 5)( x ) Q> xy x 4y x(y ) 4(y ) (y )(x 4) j> ab 7b ac 7c b(a 7) c(a 7) (a 7)(b c) - 55 -
emeronti9 smikardwerktimyymanmyygbaøat lmhat;!>ekmansmikar x, 5 (x ) 8, x 4x 0 nig x (x 5). etismikarnaxøhcasmikardwerktimyymanmyygbaøat? @> edahrsaysmikarxagerkamrycepþógpþat;cemøiy ³ k> 5 x x> 40 n 70 K> m.. 5 X> y 4 9 g> 8 y 56 c> 6 x 48 q> 0 7x x C> 8 t Q> 5 0. #>edahrsaysmikarxagerkam k> 5(n ) 5 4 (n 5) x> x 5 6x K> 5 y 9y 0 y X> (4x ) x 6 x 40 g> 0.05x 0.4 0. 5 c> (y ) 5 4y q> 5( y) 7 4( y) 7-56 -
emeronti9 smikardwerktimyymanmyygbaøat $> edahrsaysmikarxagerkamrycepþógpþat;cemøiy ³ k> 5 x 0(x ) 40 x> 5 4(t ) (t 7) x x K> X> x 5 x 7 x x 4 6x g> c> 4 4 8 x x x x x x x x q> C> 4 5 5 4 %> ctuekanekgmyymanbenþayesµinwg 4 m ehiyépþrklaesµinwg épþrklakaeredlmanrcugesµinwg m. KNnaTTwgctuekaNEkgenaH? ^> m:asiunftmyymantémø 7duløa bnþab;bibba úhtémø 0 %. etitémøedimrbs;m:asiunftenahesµinwgb:unµan? &> FugBIrmansaMg 50 lit. ebiekyksamg litbifugtimyy nig yk 5 litecjbifugtibirenahfugtamgbirenasl;samgesµikña. etifugnimyy²mansamgb:unµanlit? *> KNnabrimaRtRtIekaNmYy ebirtiekanenahmanrgvas;rcugtimyy esµinwg 6 m rgvas;rcugtibiresµinwg 7 énbrimart nigrcugtibiesµinwg énbrimart. - 57 -
emeronti9 smikardwerktimyymanmyygbaøat (>LanmYyecjdMeNIrBIPñMeBjeTAkMBg;camEdlmancm ayesµinwg 4 km edayel,ón 65 km / h ehiylanmyyetotecjdmenir Rcas;KñaBIkMBg;cammkPñMeBjedayel,Ón 45 km / h. ekdwgfalantamgbirecjdmenirenaebletmyy. k> rkcm aybipñmebetakenøgcybkña? x> etib:unµanem:agerkaymketiblantamgbircybkña?!0> plbukbircmnynesµinwg 4 ehiybirdgéncmnynti! buknwgcmnynti@ esµinwg 6. KNnacMnYnTaMgBIrenaH?!!> vir³ekµgcag»bukrbs;kat; 4 qñam. ekdwgfaryhebl@qñametotpl bukgayugñktamgbiresµinwg 40 qñam. rkgayu»buk nig Gayurbs;vIr³ > - 58 -
emeronti9 smikardwerktimyymanmyygbaøat dmenahrsay!>ekmansmikar x, 5 (x ) 8, x 4x 0 nig x (x 5). etismikarnaxøhcasmikardwerktimyymanmyygbaøat? smikaredlcasmikardwerktimyymanmyygbaøatkw³ x nig 5 (x ) 8 @> edahrsaysmikarxagerkamrycepþógpþat;cemøiy ³ k> 5 x ek)an x 5 x 6 epþógpþat; 5 6. ducenh 6 Bit x. x> 40 n 70 ek)an n 70 40 n 0 epþógpþat; 40 0 70-59 -
emeronti9 smikardwerktimyymanmyygbaøat 70 70 Bit n. ducenh 0 K> m.. 5 ek)an m.5. m 0. epþógpþat; 0... 5.5.5 Bit ducenh m 0.. X> y 4 9 ek)an y 9 4 y epþógpþat; 4 9 9 9 Bit ducenh y. g> 8 y 56 ek)an y 56 8 y 5-60 -
emeronti9 smikardwerktimyymanmyygbaøat epþógpþat; 8 5 56 56 56 Bit y. ducenh 5 c> 6 x 48 ek)an x x 48 6 epþógpþat; 6 () 48 ducenh 48 48 Bit x. q> 0 7x 0 ek)an x 7 x 6 epþógpþat; 0 7(6) ducenh 6 0 0 Bit x. - 6 -
emeronti9 smikardwerktimyymanmyygbaøat x C> 8 7 ek)an x 8 7 x 6 6 epþógpþat; 8 7 8 8 Bit x. ducenh 6 t Q> 5 0. ek)an t 5 0. t 0.55 0.55 0. 5 5 Bit t 0.. epþógpþat; 5 ducenh 55 #>edahrsaysmikarxagerkam k> 5(n ) 5 4 (n 5) 5n 0 5 5n 5 5n n 4 n 5 n 9 9 5-6 -
emeronti9 smikardwerktimyymanmyygbaøat 7n 4 4 n 7 n x> x 5 6x x 6x 5 4x 8 x x 8 4 K> 5 y 9y 0 y 5y 9y y 0 5y 5 5 y 5 y X> (4x ) x 6 x 40 8x x 6 x 40 8x x x 6 40 x x x - 6 -
emeronti9 smikardwerktimyymanmyygbaøat g> 0.05x 0.4 0. 5 0.05x 0.5 0.4 0.05x 0.5 x x 5 0.5 0.05 c> (y ) 5 4y 6y 5 4y 6y 8 4y 6y 4y 0y y y 8 0 0 0 q> 5( y) 7 4( y) 5 0y 7 8 4y 0y 4y 0y 4y 6y 4 y 4 6 8-64 -
emeronti9 smikardwerktimyymanmyygbaøat $> edahrsaysmikarxagerkamrycepþógpþat;cemøiy ³ k> 5 x 0(x ) 40 5x 0x 0 40 5x x 60 60 5 x> 5 4(t ) (t 7) K> 5 4t 8 4t 4t t 5 t 8 t 5 9 4 t 4 8 t x x 7 x x 7 x x 7 7x 7 x 4x 7 x 7 4-65 -
emeronti9 smikardwerktimyymanmyygbaøat X> g> x 5 x 9 x 5 x x 5 x 4x 4 5 x 4x x 5 4 x 9 x 9 x x 4 4 8 (x ) 4(x 4) 8 8 x 6 4x 6 8 8 x 8 8 x x 9 x 9-66 -
emeronti9 smikardwerktimyymanmyygbaøat c> x ek)an 6x 4 x 4(x ) 6x x x 8x 4 6x 8x 6x 4 lkçxnð x 0 x x minyk x x x 4 5 0x 0x 6x 60 4x 60 60 x 4 0 x 7 x x x 5 4 0(x ) 4(x ) 5(x ) q> C> b x 0x 0 4x 6x 5x 0 5x 0 x - 67 -
emeronti9 smikardwerktimyymanmyygbaøat %> ctuekanekgmyymanbenþayesµinwg 4 m ehiyépþrklaesµinwg épþrklakaeredlmanrcugesµinwg m. KNnaTTwgctuekaNEkgenaH? cemøiy KNnaTTwgctuekaNEkg tag x CaTTwgrbs;ctuekaNEkgenH tambrmab;ek)ansmikar ³ 4x 4x 44 x x 44 4 6 ^> m:asiunftmyymantémø 7duløa bnþab;bibba úhtémø % etitémøedimrbs;m:asiunftenahesµinwgb:unµan? cemøiy tag x CatémøedImrbs;m:asIunft 0 ek)ansmikar x x 7 00 7 00 ektaj)an x 90 duløa. 80 0. - 68 -
emeronti9 smikardwerktimyymanmyygbaøat &> FugBIrmansaMg 50 lit. ebiekyksamg litbifugtimyy nig yk 5 litecjbifugtibirenahfugtamgbirenasl;samgesµikña. etifugnimyy²mansamgb:unµanlit? cemøiy tag x nig y CacMNuHsaMgkñúgFugTImYy nig FugTIBIrerogKña tambrmab;ek)ansmikar ³ x y 50 () ehiy x y 5 nam[ y x 5 x () yksmikar ( ) CMnYskñúg ( ) ek)an x x 50 x 50 x 8 x 8 64 ehiy y 64 86 ducenhfugtimyymansamg 64lIt nigfugtibirmansamg 86lIt. - 69 -
emeronti9 smikardwerktimyymanmyygbaøat *> KNnabrimaRtRtIekaNmYy ebirtiekanenahmanrgvas;rcugtimyy esµinwg 6 m rgvas;rcugtibiresµinwg 7 énbrimart nigrcugtibiesµinwg énbrimart. cemøiy KNnabrimaRténRtIekaN ³ tag p CabrimaRténRtIekaN ek)an p 6 p p p p 8p 7 6 6p 7p 6 p p 6 6 8 4cm ducenhbrimartrtiekankw 4 cm. - 70 -
emeronti9 smikardwerktimyymanmyygbaøat (>LanmYyecjdMeNIrBIPñMeBjeTAkMBg;camEdlmancm ayesµinwg 4 km edayel,ón 65 km / h ehiylanmyyetotecjdmenir Rcas;KñaBIkMBg;cammkPñMeBjedayel,Ón 45 km / h. ekdwgfalantamgbirecjdmenirenaebletmyy. k> rkcm aybipñmebjetakenøgcybkña? x> etib:unµanem:agerkaymketiblantamgbircybkña? cemøiy k> rkcm aybipñmebjetakenøgcybkña tag x Cacm aybipñmebjetakenøgrfynþtamgbircybkña ek)an 4 x Cacm aybikmbg;cametakenøgcyb. x 4 x ek)ansmikar x>cmebah 806 65 45 9x (4 x) 9x 6 x x 6 x 6 806 km x 806 806 t. 65 65 75 x ek)an h - 7 -
emeronti9 smikardwerktimyymanmyygbaøat!0> plbukbircmnynesµinwg 4 ehiybirdgéncmnynti! buknwgcmnynti@ esµinwg 6. KNnacMnYnTaMgBIrenaH? cemøiy KNnacMnYnTaMgBIr tag x CacMnYnTImYy nig 4 x CacMnYnTIBIr ek)ansmikar x 4 x 6 nam[ x. ducenhcmnyntimyyesµi nigcmnyntibir 4.!!> vir³ekµgcag»bukrbs;kat; 4 qñam. ekdwgfaryhebl@qñametotpl bukgayugñktamgbiresµinwg 40 qñam. rkgayu»buk nig Gayurbs;vIr³? cemøiy tag x CaGayurbs;vIrH nig x 4 CaGayurbs;»Buk ek)ansmikar ( x ) (x 4 ) 40 x 8 40 b x 6 ducenhvirhmangayu 6qñaM nig»bukmangayu 6 4 0 qñam. - 7 -
emeronti0 lmhat;!>erciserisvismpabkñúgsmenrxagerkam ³ vismpab < ; 8 > 5 ; a b ; c < d ; a c < a d,a c a d @> bmebjsbaøa > b <, enakñúgrbgb;xagerkam ³ k> 0 < 0 enah 0 4 0 4 x> a < b enah a c K> a > b enah a c b c b c X> < enah 4 4 g> 0 < enah 0 ( 4) c> a < b enah a c b c ( 4) q> a > b enah a c b c cmebah c > 0 C> a > b enah a c b c cmebah c < 0 #>bgðajfaebi a > b nig c > d nam[ a c > b d ryc[]tahrn_caelxbba ak;. $> bgðajfaebi a > b nig c < d nam[ a c > b d ryc[]tahrn_caelxbba ak;. - 7 -
emeronti0 %>bgðajfaebi a > b nig b > c nam[ a > c ryc[]tahrn_caelxbba ak;. ^> erboefobcmnyn ³ 5 7 7 k> nig x> nig 7 4 7 55 7 K> nig 5 X> nig &> a 0, b. epþógpþat;fa a b a b? vismpab - 74 -
emeronti0 dmenahrsay!>erciserisvismpabkñúgsmenrxagerkam ³ vismpab < ; 8 > 5 ; a b ; c < d ; a c < a d,a c a d cemøiy smenredlcavismpabman ³ <, 8 > 5, a < d, nig a c < a d. @> bmebjsbaøa > b <, enakñúgrbgb;xagerkam ³ k> 0 < 0 enah 0 4 < 0 4 x> a < b enah a c < K> a > b enah a c > b c b c X> < enah 4 < 4 g> 0 < enah 0 ( 4) c> a < b enah a c < b c > ( 4) q> a > b enah a c > b c cmebah c > 0 C> a > b enah a c > b c cmebah c < 0-75 -
emeronti0 #>bgðajfaebi a > b nig c > d nam[ a c > b d ryc[]tahrn_caelxbba ak;. cemøiy ekman a > b nam[ a b > 0 ehiy c > d nam[ c d > 0 ek)an ( a b) (c d) > 0 ducenh a c > b d. ]TahrN_Caelx ³ yk a 0, b 7, c 9, d 5 ek)an 0 > 7 nig 9 > 5 ducenh 0 9 > 7 5 9 > Bit. $> bgðajfaebi a > b nig c < d nam[ a c > b d ryc[]tahrn_caelxbba ak;. cemøiy ekman a > b nam[ a b > 0 ehiy c < d nam[ d c > 0 vismpab - 76 -
emeronti0 vismpab ek)an ( a b) (d c) > 0 ducenh a b > b d. ]TahrN_Caelx ³ yk a, b 7, c 9, d 5 ek)an > 7 nig 9 < 5 ducenh 9 > 7 5 4 > Bit. %>bgðajfaebi a > b nig c ryc[]tahrn_caelxbba ak;. cemøiy ekman a > b nam[ a b > 0 b > nam[ a > c ehiy b > c nam[ b c > 0 ek)an ( a b) (b c) > 0 a c > 0 ducenh a > c. ]TahrN_CaelxbBa ak; ³ yk a 7, b 0, c 5 ekman 7 > 0 nig 0 > 5 ducenh 7 > 5 Bit. - 77 -
emeronti0 ^> erboefobcmnyn ³ k> 5 nig 7 5 7 eday 5 < 7 ducenh <. 7 x> nig 7 8 ekman eday 8 > 7 ducenh 7 4 7 K> nig 5 4 70 ekman nig 55 eday 70 < 77 ducenh 55 7 X> nig 605 ekman 7 77 5 55 4 7 <. 5 7 >. 7 55 nig 4 55 7 >. 7 4 vismpab ducenh &> a 0, b. epþógpþat;fa a b a b eday a b 0 9, a b 0 ducenh a b a b. - 78 -