K8 8EPB QBH DEDEHE KONHKN8E KR OSTUVWXRY NZZTWT[\SX\T]^ AY_T^WXRY `YS RX DV_RTX. abyct^wy byd^wexf. bb8ob8mn

Hasonló dokumentumok








+ $& (, -!./0 1 )- 1! * 2 $& (, -3 %% 3% %$(%$, (%& /.+ %# &&-34# # $& (, -# %% #%$#% % 0( 5* 6 #6# # *33777# 4# 8-$( %(' $ $%'$ 9 # :+!! %%, # "#$% &





!"# $%& % # ' & & () *+%,&- +,.! "#$%&'" $ ()*+/01, 8 -. /01 )% )9 ABCD E )% ) ():; ) 3 : <3 "#$ => : '" A B CD E CD A ) FG


ó ó é ő é ő é é í á ú óé ü ö ö é ő é ő á á é ü ü é ő í ó í ú Í í ö á ő á á ú ő á í á é é á í é é á é á é ó á ö é í á á é é é á á é ó é é ő í í á í ó ő


Ú ű Á ű

ó í ó é é ó ö é ö ű ó é é é á é é é ú ő é á é ó ö á é é é é á á ö ú ő é é í é á ő é ú Ö í ö á á ú é é á á ö ú ő é á á á é é ó ö ú ő é ö ű ő é ő ó ű ő

!"#$ %#"&$' ' &&#""" $!&!"#$&" &""!"#$%&' ()*+,-./0!"#$$( #!"#$%&' #! #! ) #! #! ) #! ) $ # 1 234)!$""$#! :; 34)!$""$#$ 1 <34)!$""# =>! #



á é é é é é é é é á é é é é á ú ó é ő á ő á é ű é á ó é é ő é ú ő á é é őá é é é é é é é á ő ö ő ö é á é ő é éé é é é á ő á é ő é á ó á ú á á é á é őí


!"# $% & ' &#!"# $% &' ()*+,-./01' :; ) <& ' E : *B 1) F GF&HI ; J9:KLMNO ) $ '; ) & P QRS T$ U8 1VI W&)F(XJY KLMNO ) F P ( Y &)

!" # $%&'! "#$% &' ()*+,!-./ 01 $% :; &' ()*+, -./( 0()*+, $ :; 0()* < =>?-./( 0()*+, = 0()F GHI $J K

í ö ö í ő ď ż ö í Í ő ť ö ü ľ í ő Ĺ í í ÍĹ Í É ő Ę ő ľ Ü íľ ő Ę ľ í ő ő Í ő ľü í ú í ő ľő ő Ĺ Ĺ ő ő ľ ü ő ü ö ő ő ľ ü ć ő ľü ľ í ő ő ü ő ö ľ É Í ö ö ő


+,-!.,/#0-! "-',/,-0 )45 1 # 1 11 #// 5(( &!.! &' & ()&**!& &&&!"#$%!" # $%&' () $% # *+,-./)!" # 01 + ) !" :; 89 DE3 689! * F


ÙS #!Ë 3H )*+,- r Q# m 89:; 9 K6700'9:;6Õp 4G550 q 6 µ # m89:; 700 RS& ÚÒ

, - &' $ ' ' () $ * "+ ) ",.+/ % - %0. / ( 1 $ $!+'!"##$!%!!!!!" #$ %& ' ()*" #$ %& +!"#$%&' ( )*+,$%& -./# ,89 :; $' ). :$%& AB

!"#$ % & ()*+,-. ' $1 /0 1!" #$%&' " ()*+,-./01! "2 % :; E 89 ()*FGH IJKLMN89 O + 1 P QRSTUVW XY!" #* = () QZ[VW XY\ ]^_ `1 abc!"89

+*!+ !#!**= *,-.34[\ » '" '!e 4, S > ; " ! 5 < c! ]ùþn WwiNth. n ; < Eyï. %! jõ t,-.kl B! +>


! *+,-./01! " #$%& % $'! $ $ % $ % % $, ()* 89& : + :, ; * / 8 < - : ( ; 5 => A - BC2)DE 5 /IJK L MNO ) P C234 QR STUVW

THE LITERARY WORKS OF ŚRĪMANTA ŚAṄKARADEVA AND MAHĀPURUṢA MĀDHAVADEVA

Í Ú É Ö Ö ý ä Ö Ö Í É Ö Ö ľľ ľ ľ ŕ ľ ľ ä ť ä














































!"#$$%" $$$& '$"%!"#$%& $ $! "!"$## "!"#$!!$###& ' %&' ()*+, (-./ (01 ()./ :; # < BC DE :; 0 * %% +,$#+ " *-. '" --&*


mo2gh?, ²>Ö ØC #$ ÙÚÆ/ÛÜÝÞßà&áâÖ:3opã6sä/åæ, çùè& TmnÈé ~êë z²³ìíopîïïðð &ñ òóôõö( / øùúc}û, i ü ±¼


KockaKobak Országos Matematikaverseny 8. osztály


' 0.*)& )0- ) $ &!"# ' $% : 01 #$ % ; : 456 &!"#$%&' ( )*+,- ( )' *+ $, - ),,".') / ' *!./ :; &!"#$%&' ( + + <= DE 0 1' #


! "!"#$%&' (!")* )*0 1. )* ,89:; = % ( :; )* F:;GHIJKL-MNO PQ-RS TJUVWXY F ) J-M NO :;- Z[\]^9_`abc ) L - Z:;GHIJ J -/ ) J1 )

; #044 ( 0! "!"#$# %&' %!" ()*+,-.,'/ :; ABCDE F GHIJ7KLMN () O ; ( ) PQ1 # $ R ()STUV9 WXY N # $ R () M Z[ \] # $ R () ^_`



IV. Algebra. Algebrai átalakítások. Polinomok

!"#$ %&' " $ () *+ *,-./0 ( !"8 9:; < BCDE? FG < O = ; 5PQ RST? UVW "8XY=? Z[\]^_` < O 3?; < -? L "8XY Z[\ I <




Átírás:

()**+,-./0,+2342546275 89;<<=>?@;<=ABC9DAEF9GEHH9 89;<@IJ?@;<IABC9AKG9 A B D L M M H KG N KO N H KN 8 N K88EPBQBHDEDEHEKONHKN8E KROSTUVWXRYNZZTWT[\SX\T]^AY_T^WXRY`YSRXDV_RTX abyct^wybyd^wexf g.hi0j)j-,./0+.hiklkj/k bb8ob8mn l)+i,-0il0j)nki0o,ikp,l/i0pkjki.+k763qok+6273rhi0h0l/0o.s tuvwwvwslxix+xr,jhkil0j.ok++kp.+ki.hhiklkj/.j/khx/xri.hhiklkj/./0k o,ykl0o.+z.{{x,.-0n0}.+.r-0jo0n,-,+,0k+k/0hikl0,+l)0l/)o,0,j ~.i,r.+.{,.),j/,j0wk+.jx q ƒ ƒ ˆ,kjo.w.j,/.i,. 0-.+ko,Š.i.j/0r,jhkil0j.ok++kp.+ki.hhiklkj/.j/k hx/xri.hhiklkj/./0ko,ykl0o.+z.{{x 0nkj,-0wknki.i0r-0j)y,-,0,j Š.i.j/0r.+{,.+k},ip,+,0 7ko0n,-,+,0o,p,/.+kk+k/0.+z,jo,i,ˆˆ0(xkx-xŒ lknki.i0xo0nkj,-00i.{/.x+kp.+n.,+x,/ Ž ƒ ƒ 0lh,/.+w-,kj/,y,- 0jl)+/,jplxix+xr l)/ )i0hklxhx.xrj0j-0l/,/),/,,j p,)o,ˆ,0 Ž šž ƒ sok+.ok/kin,j.ˆ,0jkr-0n)j,-./.-0jj0/..y,in.ok+ xœx(xkok+ o,ik/0ikok+z ik.pkl/,0jkok+h./i,n0j,0ok+z xwx xo,š.i.j/0rhi0/xjx 275q 3qok+7j0{kn*ik6273ro,kl-+)l,0jkok+.i,-0ikj/ko.+. 678929797772972228928279272229826!"14#"$&8'467 0205

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àb`de^bà(,)5/-.)/1/-39./1)*/443 (,)5/2*)431.)/-3()*1,73*)1*(,-3+E,,-37(*7313F37(,+3/53713+3(,)5/ 1)/.8/1*5*?3,8/1,)3/53/++,7*)3,+*),5/137,)F363:(,)5,,73?,46,-,5, 71).1.),7/431/)3,-,5,G63,4-,7/431/)3,,-*7(,-/53,),-3J/)3:J/)5,1/K G4-)3/KL)/43:J)34-373:M*??3/:I,++,:L/)/41*:N7(,-/53P3.4313-3M*??3/,R*53+5343+*-3J/)3< 678929797772972228928279272229826!"14#"$&8'467 4205

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`7-7*8,=*-<,8.-7@48A+*-64;-67-<;Q8,=.+3-:8:+ 34;Q4+6+68<878,3-4.@68;838,*8@8,+.8647+.8,*8,8.*89@-83-6+9+44. 68+*-87*4,*-<4,:4++=*-9+*4;+0 a8747*8:+./(010205(<7-7*8,8,3-.+@48,+.8a4*494*?38.@6-::83498,*- 49@=A,+*-0 bq4+9+*-4.64;-67-<+.+;+986+34;-,74a.4-38.hc34;89j68klhv<./47*+,b+;+=*8.+68<;-,-634,+,b+38.564j=,+.8<d7*+*+687@4,*+<@86;qe 4,>-,3+*+4,3464*-0 (@@8.+*+./-634,+,B+34@649-A6+3-<4.b-,74A.4-341*+*-<@=63+,3-+*- 34=,;-,*6+7*-A4=647@6=38,B4+.8<;-,-634,+,B+38.KOA8,,+4-KLHP,0 MVI<Q+687@4,*-4.A6+:+98<64*8,8,3-.-4,>-,3+*-<4,f=+,*-./+6*0MP< ;-99+K<38.38;68*-.8A47.+*4:-,0HOM38.KLLO70904087-,86+4 ;-,;-68,*4@+6*8;4@+,*4+3=,+@6-;83=6+34A+6+@86./+>43+98,*-34=, +@@+.*-@=JJ.4;-3+.34;Q4+6+68@68;838,*4@8,+.4<7-.*+,*-;-,64>86498,*- +.84@-*8743468+*4g34;Q4+6+*487*4,*4h<3-@-.+;-,3+,,+7*87+0 678929797772972228928279272229826!"14#"$&8'467 $205

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`QVT_^QK6N/*/>@21.90.2442*@20@.266/@.09KO,2*/4A9H2 >,L.6./0@/-/*2.0>,>.>@/012-.,0262,>2-./>6*,>.90/4/A6B-B.0.-90/.@a M9A2*/ZTWQXbcM2062012-.@2*,0/690-200/4/02*.QbXTdT^T_[K.*6/A@.L.62@9 -/*62>/*2A.98.,-.1.2*/K@20@9.0-/A9822*2RQ\]^_\QUQR_^Q-/*-.H./@9-. 4A9-,1.90/2*/4,55*.6N/2MM.0.>@A21.90.-.6/A@.L.62@.K>@25.*.@9-2*+2A@B e;-/*-b4bab:=-.6/m5a/:;;;0beeyb f+2a@b7=k69mm2<k*/@b6[k-/*6.@2@9-/6a/@9*/8.>*2@.h90b<j7/>6*,-/ -2*242A@/6.421.90/2*/4A96/-,A/2-/H.-/0124,55*.62-.2L.-2M/0@9-. 2442*@.8*.94/A2@9A./6909M.6.K4/A.O,2*.690A.L/A.M/0@92@2*,0.>988/@. O,2*.L.62@.Z2-/>Bc2MM.0.>@A2@9A/690A244A/>/0@2012K0/*62>9-/*/ >96./@a-.624.@2*.[>.2>@2@24A90,06.2@2,02>/0@/012-.690-200242>2@2.08.,-.62@99>.209>@2@./M/>9,0-/6A/@94/02*/-.690-2002-.H/0,@9.A/H9625.*/944,A/,02>/0@/012-.244*.621.90/-/*24/02>,A.6N./>@2K2. >/0>.-/*+2A@BIGgDhhDhI6B4B4BK4/A8A2H.A/2@..0-2009-/*9h@2@99-/*2 ibjbk6n/.06.-909>,*2km9a2*.@a4a9l/>.902*/lk@a2.o,2*.?2009h/a2@2 *2IGgDhhDhIB m/a@2*/m9@.h9k*+2a@b7=k69mm2:k-/*-/6a/@9*/8.>*2@.h90b<j7.m490/ 2.620-.-2@.2*24A96/-,A2-.82A2*+955*.89-.-.6N.2A2A/.*49>/>9-/. 678929797772972228928279272229826!"14#"$&8'467 (205

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`VYSNVTUSTTSF/899)(8,4:,4),453-82,()98532)<3 584234431)2)-,13> a)(.3<)18.,98/584:,43<,.;2,-)1=<,:,537,84)2)k<,84)(,285+1)4.3<,/,< 58113?2)<8-.)-83(.>J@63=()9,-.856),<58458()4.)32+43 =(85)2+(32,K3(3/3,:,4,2)<I3(.>J@bc[QRX^X\XUXVZUXT[d[T[ZSY[O/58113 L/<).>NO/2)<2)5().8<)K,-<3.,984>LMJ/484-,3.)4+.832,42,53()/4)<3 2,56,3(37,84)/<)5842344)=)(()3.,2)=)43<,773.,/899)(8EUXN_XSZS\X [^\XT\XUV`VYSNVTUSTTS^\[^SF/4e<)5842344)()9853.)/4e*+)<)=)(<) *+3<,-,3,4.)(9)4+.3<3(,3A,<,.37,84)> J>Gf(A)4)/23<)-+(,:)(,.)2,-=8-,7,84,48(13.,9)/5845)(4)4.,<3 <)K,-<37,84),413.)(,32,3==3<.,=+AA<,5,/P56,3(856)/=)(5,g56)3.,)4) 3,()*+,-,.,2,8(2,4)K)4)(3<))18(3<)2,311,-,A,<,.;3<3=(85)2+(32, )9,2)473=+AA<,53)=)(*+34.8(,K+3(23<I3-8<9,1)4.82)K<,84)(,:8(13<, 2,285+1)4.37,84)+.,<,3<3=3(.)5,=37,84)3<3K3(3/(,<)93<3 EUXN_XSZShXVT[UX[^\XThXVT[U[YZ[S\VUV`VYSNVTUSTTSF/56)/4)<3 <)K,-<37,84)=)43<))=)43<G=(85)-+3<,-.,53/=+g)-)()()-3/-+,-.34732, =3(.)/-8<823<K,+2,5)2)<I)-)5+7,84)/3,-)4-,2)K<,3(.>MMDGMMM5>=>=>/<3 5+,=()5,=+3:+47,84)P*+)<32,2,56,3(3()<I)-.,47,84)2)<()3.8/ )-5<+-,931)4.)4)<),=8.)-,,45+,.3<)53+-3)-.,4.,93-8=(399)4K33< 678929797772972228928279272229826!"14#"$&8'467 205

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`-1, 217(4/)()34++,)3)?*,O94+,*39)3-0/2-/39)*3-+,09,*(9014/C,)54?2J4 H4145)34*,(94H)54/34145)/424*,3_1,0/)(9-/0/2,)4*(94*),/L49,3- )5),/349H4/03)4*3,/C,-/46PQb\cZ[R8d7e7f7g)C,-?*4C7D?@=L)++,- @h:i/7><>>jb-/*7w37?*4c7k?@i)+-*3-@h:</7=h<<jb-/*7w37?*4c7k? :>L)9C-@h:</7::<@jB-/*7W3?*4C7k?@i1,24L]94@h:;/7>=<ijB-/*7 W37?*4C7k?>*434L]94@h:=/7=>@ijB-/*7W37?*4C7kD?S-3-]94@h:=/7 =ES<F?2-/39)1143)1)0/)34*,L,/-9,3)9,)?)A,-9)3))/2J4/45) +,09,*(9014/C)9424/346B-/*7W37?*4C7kD?<L)++,-@h:i/7@<h=F?2J4,/H42494(03)*0A,2,4/345)2-/*3)3)C,-/4145)2,92-*3)/C)145L49-142-9*-14534L(-*0224*,H))5)*4/34/C)1,2-/1)//))(4/)*-*(4*)- ()34++,)3)?-/14(-3499,2)H)94,5L)309)3-4A43-4*3,/3,H-14594)3-?2J4 4*,L),5()9342,()/34)5)(9-24109)1,4H,14/C)(0]]5,2)1)5()54*)94,/ *4141,+)9),5(942414/34(4/)54*0],3-7 >7TW05H49*)/34145)+,09,*(9014/C)(4/)54?,/H424?5)3)5-9))*49,3) L)/2)/C)1,/424*,3_1,0/)(9-/0/2,)4*(94*)145+,01,24 678929797772972228928279272229826!"14#"$&8'467 1205

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Àà-0\ ;12)6*;684)-0;624)6*6;81-)(.866()70()2/6;.BB*0-6*+12)8)(0 ;8)5.208,0(6)7)24.6*0-124),46/0120(0;8)-)()240,[6718)71*0962-b)212 (0-b0686406*6,46/012)6;;6*4624)9[6-)2(170070-12,46468)*6;81;806,04.6/012)6::01826469-15;8)2()24)*)024)87)2.4)-6.,)(0),402/012)()* 8)641)c1()*6;)2696:*0)[)40()*80*6,-01()08)*64070-)840[0-640<-[8>684> @Gd@Fd@FdeJS(>;>8>2>À`-04>H912();14)8(051,4868)*6;0)26-6;6-04f6-124868)> gqhy9*6,46/012)6;;6*4624)212;.\-b)80-6768)(6z.624180,.*40;8),10* -6,)*6801:0.(0/06*)*)02[1856/0120.40*0680,-124868)*),04.6/0120,1::)407)902-.07)8,6210,1::)40Z.6*0[0-640T]MThT()*+1;)86418) )-12150-19-b);684)-0;0216(.26;81-)(.86(0:686;.BB*0-6980,.*462(1 *)8)*6407)-)840[0-6/012080*6,-064)Z.6241B6,46;)880,-124868)*)6.41d (0-b0686/0120():*01[)8)2409-12-12,):.)24)12)8)(6;684)(0Z.),40.*4050(0640768,09;)84)5;192)*[68-12,46468)*6;81;806,04.6/012) 6::01826469027084i()*)()-*6864180)(0),402/012)(08)6401(0;)2) 02[*04)9162-186;)8*6-12-),6806B0*046/012)> 678929797772972228928279272229826!"14#"$&8'467 #205

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`_[Z[YaacY_XYad2:3.11775181/,/15.2,0.+,)/,9,)/,2 +156:8<1):<.;+.4.18.:7:9=,/,)/,23;.3/1)41+.=18/,2=:3/:7A,.57:+.7, +.=8:7,+;81=,)15,0.<,)/,8.7A.,+,2=,8561==;)/:256.).4.1/.01+,51=18/,.)/,8,31/1+.5.<,)/,215-.),+,51=8:);)7.1+,51+,75181/:8.1+.,3/.)4.:), G18/BCCC27:BP27B=B=BI2+.0,8319,)/,+15=8,0.<,)/,7:+.7,e:77:+,5 PNfO251++:0,g7:9,F,)8199,)/1/:+1517./1/1:8+.)1)41+,5K:)3.<5.: +.L/1/:2L,4B(2MC<,))1.:MOPS)BfHRg,812.)0,7,2=8,0.3/1G18/BQHS 678929797772972228928279272229826!"14#"$&8'467 3205

)*+*+*-./01-2034-56)4-/-20/7-8-9):65;<=7)7079)->6/-57)09?71470 564;6?279@7096564/6-206564-+69-* A*BC2-9264-)0>+46?72D5646E<6?27097+0?26674/746F-20)092/-?20 17</7?+/<569@7-468?<?7?20901/-F7/-17097+6/50F6/?757):7-/-/64- )0>+69?-@70965646?+6?68-7?69?7564;-/2*GH8)0>>-I8564)057)6564 +/0)6?0->>797?2/-27F08)0>679)7?05-4-?69269@-564-J0/26 )0?272<@709-46IK-+/746GLIM89*AA8?-4F04;096/6564+-1->6920564 )092/7.<20<97=7)-20):68-7?69?7564;-/2*IN8)0>>-HBOPQ85645*R*S*NL >-1170GLLG89*IIT8U+0?2096)6?-/7->6926879F7-56=79727F-8-)-/7)0 564-+-/26?0))0>.6926* R*V*W* X4Y/7.<9-46Z>>797?2/-27F0S61709-46+6/4-R<147-[C6@7096?6)095-38 56=79727F->6926+/09<9)7-950?<4/7)0/?08)0>6796+71/-=6+/0+0?20840 /6?+7916* C+6?6)0>+69?-26* J092/7.<20<97=7)-202/-?=<?0* \/579-):64-+/6?6926?69269@-?7-6?61<72-5-4;Z<20/72D->>797?2/-27F-* S7269<20):6?<?7?2-907+/6?<++0?2757)<7-4;-/2*GG8)0*M85*41?*9*IKH 564GLLN?*>*78>-95--4-C61/626/7-57+/0)656/6879E<-4?7-?77+026?757 57=<?7096564-+/6?6926?69269@-8-4;0?)</->692056461696/-472D8 909):]57E<-4?7-?7-42/05-20750960-/7F64-/64;7569272D6575-2717<57@7-/7 /7=6/7.747-4-?0)762D/7)0/692665-4/-++/6?692-926461-46564-?26?-* J0?^56)7?079_-/7964-)->6/-57)09?71470564170/90N4<1470GLIM)09 4;7926/F6920567>-17?2/-27` a7<?6++79-z5->08r/6?756926 b09-264-y6?27978s6=6/695-/70 c0/69@0x6f-8s6=6/695-/708d?269?0/6 fghijhkilmh fqrstuqnsvw nfomhinphkjh xyz{s ytw}~wq 678929797772972228928279272229826!"14#"$&8'467 (205

)*,-./-01/)2 678929797772972228928279272229826!"14#"$&8'4% 05205

2025 © DocPlayer.hu Adatvédelmi irányelvek | Szolgáltatási feltételek | Visszajelzés