专题02 整式与因式分解-三年（2020-2022）中考数学真题分项汇编（全国通用）（解析版）

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15@X3_4X=X(X2-4)=X(X+2)(X-2),L⚪@টBᑖV(WX()ḄX(ᚖXYVᦑ?⚪Ꮇ⚪@ঠ[\ᦪ&77-Iᙠ^ᦪᑁᨵᑣx-120,ᓽxNl,L⚪@.••Ꮇ⚪Ḅᦪ2.ᦑ⌱9Cூab௃c⚪d⌕ὃgIḄḄ!"#⚗Ḅ%&ᑖᚖ()ᳮḄ+,-.᪷&ᨵḄᩩ0hijklᐵnoa⚪Ḅᐵp.22.(2021•qrst)#⚗&2/_4/+2%%&ᑖD()A.2x(x-l)2B.2x(x+l)2C.x(2x-l)2D.x(2x+l)2ூᫀ௃Aூ᪆௃ூᑖ᪆௃ᐜvwx%&2x,yᑭᵨ|ᐰBx&~Ḅ&%&ᑖᓽ5ூ8௃92X3-4X2+2X=2X(X2-2X+1)=2X(X-1)2ᦑᫀ⌱9A.ூab௃c⚪ὃgIvx%&x&%&ᑖ.ᵨx&ᑖ%&⚪Ḅᐵp.23.(2021.ḝ)ᓄ(1+Kᓝ-Ḅ()Ia-\)at-1.,0஺+1a-la+1A.(j+1B.------C.-----D.—x-aaaூᫀ௃Bூ᪆௃ூᑖ᪆௃ᐜᑖᔠy~◀%&ᑖᓽ5ᑖᓄ.ூ8௃9?&-tlxl^MZ,2xg+lMa-D,a-\cva-\a2a

16ᦑᫀ9B.ூab௃c⚪ὃ¡ᑖ&Ḅ¢"ᓄஹ%&ᑖ¤Y¥Ạ⚪§¨Wᜧ.⚪ᐵpjkᑖ&Ḅ¢"ᑣ.24.(2020•ª«¬)®ᑡ#⚗&°¢ᵨBx&ᑖ%&Ḅ()A.a2+b2B.2a-h2C.-a2+b2D.-a2-b2ூᫀ௃Cூ᪆௃ூᑖ᪆௃᪷Bx&Ḅ)ᑨ3ᓽ5@ூ8௃Aஹ?&W°ᑭᵨBx&%&ᑖW±ᔠ⚪@8ஹ?&W°ᑭᵨBx&%&ᑖW±ᔠ⚪@Cஹ?&=S-a)3+஺)°ᑭᵨBx&%&ᑖ±ᔠ⚪@஺ஹ?&W°ᑭᵨBx&%&ᑖW±ᔠ⚪ᦑ⌱9C.ூab௃c⚪d⌕ὃgIBx&Ḅᵨ²ᑨ3⚪Ḅᐵp.25.(2020.³ᓭµ□)®ᑡ%&ᑖḄ()A.a(a-b)-b(a-b)=(a-b)(a+b)B.a2-9b2=(a-3b)2C.a2+4ab+4b2=(a+2b)2D.a1-ab+a=a[a-b)ூᫀ௃Cூ᪆௃ூᑖ᪆௃ᑭᵨvx%&ᑖ%&Bx&H·|ᐰBx&ᑖᓽ5¸ᑮᫀ.ூ8௃Aஹa[a-h)-b(a-b)=(a-b)(a-b)=(a-h)2,ᦑº⌱⚗┯¼;

17Bஹa2-9b2=(a+3b)(a-3b),ᦑº⌱⚗┯¼@Cஹa2+4ab+4b2=(a+2b)2,ᦑº⌱⚗@Dஹa2-ah+a=a{a-b+\),ᦑº⌱⚗┯¼.ᦑ⌱9C.ூab௃º⚪d⌕ὃgIx&vx%&ᑖ%&ᐵpÀÁ9²x%&Ã.⌕vÄ@ᐰÅÆÇÈ,ᶇ1ÊÅË9vÌ⌕ÍÎ᜻Ꮤ.26.(2020.ᑁℳÓÔ)Õ®ᑡ⚪Ö×ØwÃL⚪Ḅᭆ᳛()(1)ÛᳮᦪÆÛ▲ᦪ@(2)%&ᑖÝ-a=a(x+l)(x-l)@(3)áâ1cmḄåḄ⊤☢èéêḄᕜâÃ)14cm@(4)ìâ20ícm,☢240mm2ḄᡧÍḄᙊðñ120஺.A.-B.C.—D.1424ூᫀ௃Cூ᪆௃ூᑖ᪆௃ᑖôᑨ3ᔜ⚪ḄLᎷyᑭᵨᭆ᳛x&6.ூ8௃9(1)ÛᳮᦪÆÛ▲ᦪL⚪(2)%&ᑖor?-a=a(x+l)(x-l),L⚪(3)áâ1cmḄåḄ⊤☢èéêḄᕜâÃ)14cm,L⚪(4)ùᡧÍú(Dr,ᙊðñDn,9ìâ20ücm,ᑣ=20ü,ýJnr=3600.180njrr';☢240ícm?,ᑣ×-240íý”=360x240,360|J—==ᙢ"4஺=24,ijn=3600+24=150°,rnr3600ᦑᡧḄᙊ!150஺"!Ꮇ$⚪,

183ᑣ'()*+,!-$⚪Ḅᭆ᳛!T"4ᦑ⌱C.ூ56௃8⚪ὃ:;$⚪Ḅ-Ꮇ"ᭆ᳛"ᡧḄ<=>☢@"Aᳮᦪ"DEᑖG"HIJKLM"NO5PQ"RS+T"G⚪ḄᐵV!WᵨᡠZNOᑨ\ᔜ,$⚪Ḅ-Ꮇ.^ஹ`a⚪27.c2022•efghijkm4^m2=.ூlᫀ௃m2ூG᪆௃ூᑖ᪆௃᪷pqrᦪsḄ◀uWkuᑣᓽwxy.ூzG௃Gm4-e-w2-nV.ᦑlᫀ~.ூ56௃8⚪⌕ὃ:qrᦪḄ◀u"qrᦪḄ◀uuᑣ!G⚪ḄᐵV.28.c2022•ᔡ᪍iᳫ10,ᳫ",ᳫ(ᐗ"+ᐳ◤⌕ᐗ.cᵨ(ḄᦪE⊤iூlᫀ௃10mூG᪆௃ூᑖ᪆௃᪷p“ᵨ=ᳫḄᦪx,ᳫḄ”ᓽw.ூzG௃Gᵫ⚪¡•ᐳ◤⌕Ḅᵨ~10¢ᐗ"ᦑlᫀ~10"”.ூ56௃8⚪ὃ:;ᑡᦪE"H¤¥y¦ᐵ§!G⚪ᐵV.29.c2022ᜩªijkcM+1icM-1iḄ¬¦®.ூlᫀ௃18ூG᪆௃

19ூᑖ᪆௃᪷p¯I°±EᓽwxG.ூzG௃G(719+1)(>/19-1)=(719)2-12=19-1=18,ᦑlᫀ~18.ூ56௃8⚪ὃ:;¯I°±EḄ²ᵨ"³´¯I°±EḄKLE!G⚪ḄᐵV.30.(2022•µ¶·¸)ºNa+8=l,ᑣᦪE/-/>2+28+9Ḅ»~.ூlᫀ௃10ூG᪆௃ூᑖ᪆௃᪷p¯I°±E"¼½Eᓄ~(a+஺)(஺-3+À+9,wa+b+9,ᓽwxG.ூzG௃Ga2-b2+2/7+9=(a+£>)(a-/?)+2Z>+9=a-b+2b+9-a+b+9=1+9=10ᦑlᫀ~10ூ56௃8⚪⌕ὃ:;¯I°±EḄ²ᵨ"ᑭᵨ᦮JᐭÄÅGl!G⚪ḄᐵV.31.(2022•µ¶ÆÇ)᝞+,ÉᑁËÌᵨ+ÍHIÎÏ"ÐÑÒÓ"ÔAÕ◣"×ØÙ~“ÚÛÉ”,᝞Mᡠ"“ÚÛÉ”ABC஺Ḅᕜ=~26,ᑣHIdḄÝ=~.

20ADbabdCBCூlᫀ௃5ூG᪆௃ூᑖ᪆௃13ÞHI“ஹßcஹdḄÝ=ᑖà~aஹbஹcஹd,ᑖàxb=^c,c=^d,ᵫ“ÚÛÉḄᕜ=4d+2c=26,ᑡEjkᓽwxG.ூzG௃GÞHIábஹcஹdḄÝ=ᑖà~aஹbஹcஹd,•"ÚÛÉ"A8CZḄᕜ=~26,.4d+2c=26,a-2b,c-a+b,d-a+c,.,.c-3b,53/.d-2b+c=-c,ᑣc=14,:.4d+—d-26,5/.d=5,,HIdḄÝ=~5,ᦑlᫀ~5.ூ56௃8⚪ὃ:;᦮E¢âḄ²ᵨ"ã-äåM"᪷p=IḄᕜ=±EæçyᡠxḄlᫀ!G⚪ḄᐵV.32.
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21ôõᑭᵨïᐰ¯I±ExG.ூzG௃GöᦪE/+.2t-Y2ab+4ø!+,ïᐰ¯IE"a2+.2t-N2ab+4b2=a2+2-a-c±ú+
±2û2=
a±2b22,•*.2z—1=±4,53Gᡈf=-2253ᦑlᫀ~òᡈ-òூ56௃8⚪ὃ:;ïᐰ¯I±EḄWᵨ"³üïᐰ¯I±EḄᱯ5!G⚪ḄᐵV.33.
2022•·þi▅ᩞᧇ᦮ᦪᵨḄ.᝞“3a-6=2,ᦪ6a-%-1Ḅ.”᪵4l=23a-b-l=2x2-1=3.᪷"▅ᩞᧇ$%&⚪(x=2ᐵ*xḄᐗ,-av+8=3Ḅ$ᑣᦪ4a2+4ab+b2+4a+2b-lḄ.ூ0ᫀ௃14ூ᪆௃ூᑖ᪆௃ᐜ᪷"x=2ᐵ*xḄᐗ,-ax+8=3Ḅ$67U2a+b=3,89ᡠḄᦪ;<=2a+b2+22a+fe-l,9>+஻=3᦮ᐭᓽ.ூE௃x=2ᐵ*xḄᐗ,-+6=3Ḅ$2a+b=3,•••4a2+4ab+ᓃG+4a+2/7-1=2a+Z?2+2H+6-1=32+2X3-1=14.ᦑ0ᫀ=14.ூJK௃L⚪ὃNOᦪḄ᦮ᐭPᐗ,-ḄQR$9ᡠḄᦪᑭᵨTᐰVW;<

22⚪ḄᐵX.34.(2021•Z[\])2஺-56=3,ᑣ2+4஺-106=.ூ0ᫀ௃8ூ᪆௃ூᑖ᪆௃ᐜ;<6`2+4“-106=2+2(2a-5b),8ᐭ`0ᫀᓽ.ூE௃'2a-56=3,.,.2+4஺-106=2+2(2a-5b)=2+2x3=8,ᦑ0ᫀ=8.ூJK௃L⚪ὃNOᦪḄ$bc᦮ᐭd⚪ḄᐵX.35.(2021•Z[ef)᝞gᡠhijk-lhmg$(n,oᐭ1,ᑣo`Ḅpq“2X+3
>9—►►yxḄ1ᐭᔲூ0ᫀ௃11ூ᪆௃ூᑖ᪆௃9k1ᐭjk-lḄs6<9,to`$89ᡝ2ᐭjk-l6s11>9,o`0ᫀ$&⚪6.ூE௃9x=lᐭஹ=w2+2*+36x=1+2+3=6<9,to`,.♦.9x=1+1=2ᐭy=z+2x+36y=4+4+3=11>9,o`0ᫀ.

23ᦑ0ᫀ=11ூJK௃L⚪ὃNO᪷"jk-l{|}k$ᳮjk-l⚪ᐵX.36.2021•ᓅᨵᵬஹஹḄ<ᱏ᝞g.1ᵬஹᱏᔜ1ᙽ$ᐸ☢=2ᗩᗩ⌕ᵨᱏᡂiᜧ<$ᐜᵬᱏ1ᙽ$8ᱏ4ᙽ$¡◤ᱏ___________ᙽ,ூ0ᫀ௃a2+b24ூ᪆௃ூᑖ᪆௃1¤ᑭᵨ<☢W{|}kᓽ2᪷"g<Ḅ☢WḄᱯ¦$ᑭᵨTᐰVWᓽᑨQ¨©HḄ⚗$8«¨ᑮg<ᓽ.ூE௃1•••ᵬஹ®<ᱏ$ᐸᑖ¯=஺°±ᵬஹᱏᔜ1ᙽ$ᐸ☢=1+²ᦑ0ᫀ=a2+b2.2⌕ᵨᱏᡂiᜧ<$ᐜᵬᱏ1ᙽ$8ᱏ4ᙽ$ᑣ³´Ḅ☢=a2+4b2,(8H4µ¶·4i$ᑣ/+4^+4"=“+2஺2,ᑣ¶·¸¹ᡂ=஺+>Ḅ<$g<᝞ºᡠh$ᡠ¨ᱏ4ᙽ.ᦑ0ᫀ=4.

24ூJK௃L⚪ὃNO<Ḅ☢WPTᐰVWḄ»¼mR$%L⚪ḄᐵXᱞ¾WᱯJ$ᮣÀjᵨWÁ$L⚪°PᑮḄ=ÂÃஹᎷÅÆÇÈ$°PᑮḄÉÊ=ᦪ

252ab=12,/.a+b2=a2+2ab+b2=15+12=27,ᦑ0ᫀ=27.ூJK௃L⚪ὃNOTᐰVWᙠ»¼g<Ḅ¨ᵨ$ÿ
ᐰḄ⚪ᐵ.38.2022♦┶ᑖx2y-2x/+/=.ூ#ᫀ௃y.x-y22ூ᪆௃ூᑖ᪆௃ᐜ()*ᦪy,-ᑭᵨ
ᐰ*0123ᑖ.
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26ூ᪆௃ூᑖ᪆௃ᐜmᑖnᑖD-᪷WᑖḄo>ឋqrᑖᓽX.ூ9௃X+1+2,x+1x+1=(X+l)21-x+T-ᦑ#ᫀ;k2.ூ<=௃>⚪ὃ@AᑖḄ◀Bvwᑭᵨ
ᐰ*ᑖD#>⚪ḄᐵabᑖḄo>ឋqvwᑖḄB.41.(2022•cdyz)᝞}D᪗;জDঝDঞDটḄᙢᡂজCঝᔠDঞCটᔠDḄ☢5.A£=a,OE=஻Da>b.A,_____________________[DজP0ঞটNঝBC(1)a,b᦮ᦪDᑣPQḄ¤](2)¥ᦪa2—2¦-/Ḅ§;¨Dᑣ©ª%Ḅ§___________.«PQA/Nூ#ᫀ௃a-b3+20ூ᪆௃ூᑖ᪆௃(I)᪷W}⊤¯°P஺ᓽX(2)᪷W஻2-2¦-஺2=0ᑖX²(a-஻+³Xa-A-J%)஺Dµ¶·²a=஻+J%,᪷WḄ☢5,X²=Ậ=ᬯ,-01ºᓄfᓽX·.

27ூ9௃(1).জCঝᔠDঞCটᔠDAE=a,DE=b,:.PQ=a-b,ᦑ#ᫀ;a—b](2)2a6-/=0,a2-lab+b2-2b2=(a-b)2-2b2=(a-b+6b)(a-b-Q)=0,:.a-b+6b=஺ᡈa-b-6b=஺/ᓽa=(»¼)ᡈa=/>+¾b•.Ḅ☢¿5,:.EP=-,EN=-,ah(a+6).À+2](a+ÁÂ+32S…(qÄ,ÄH"”_a2+b24-lab_/+஻+/U_2aa2^b1-2aba2+b2-a2+b2b2=("Ç)ஹ3+2&.b-ூ<=௃>⚪ὃ@A¥ᦪwᐸᑖḄᓄf·§DÊËᳮ⚪ÍD_`abÎ<⚪Ḅ᪷W.(1—1—4242.(2022•ÏÐÑ)ᓄf-^ߟi.a+4a+4a-3a+2ூ#ᫀ௃Tூ᪆௃ூᑖ᪆௃᪷WᑖÒᔠÓÔḄÕÖD×3ØÔᓽX.ூ9௃a-3a2-42-Z---------------------1---------஻+4a+4a-3a+2a-3(a+2)(a-2)2--------------------------------1-(a+2)2a-3a+2a-22a______τ_________=a+2a+2a+2ᦑ#ᫀ;Ùa+2ூ<=௃

28>⚪ὃ@AᑖḄÒᔠÓÔD_`abrᑖDÂᑖDᑖḄᢈÛ⚪Ḅᐵ.43.2021.ÏᑁdÝᦪxÞßÏ-x-l=0,ᑣà-ᑗ+2021=kூ#ᫀ௃2020ூ᪆௃ூᑖ᪆௃ᵫãឋqX²f=x+lDx2-x=l,-᦮ä¥ᐭØÔX·.ூ9௃x2—%—1=0>X2=X+1>x2—x=\tX'-2X2+2021=X
X+1-2X2+2021=X2+X-2X2+2021=X-X2+2O21=-1+2021=2020.ᦑ#ᫀ;2020.ூ<=௃>⚪^⌕ὃ@ᑖḄæᵨDmãçᓄ;V=x+1Df-x=l⚪Ḅᐵ.11QI44.2021èNx^—=—JE.0

29X<-9X.15..x——=—,x6.1/1ஹD1ஹ13/5ஹ652..xkkk-=(x+-)U——)=—x(--)=--/x~xx663665ᦑ#ᫀ;-36ூ<=௃>⚪ὃ@A
ᐰ*wî*DÊËÓᵨ*⚪Ḅᐵ.45.(2021ðᓅᓝᛆ)ôxy=2,x-3y=3,ᑣZx'y-lZfy?+18;Q>3=ூ#ᫀ௃36ூ᪆௃ூᑖ᪆௃ᐜùú⚗ᑖD-¥ᐭ·§DᓽX.ூ9௃xy=2,x-3y=3,.,.Y=2>yy(x-3y)~=2x2x3?=36,ᦑ#ᫀ36.ூ<=௃>⚪^⌕ὃ@¥ᦪ·§Dab()*BC*BᑖD⚪Ḅᐵ.46.(2020ðᓭ)▅þᳮÿ(/+1)x+wᱯḄᦪᢥ☢Ḅᑖx3-(n2+l)x+n=x3-n2x-x+n=x(x2-n2)-(x-n)=x(x-ri')(x+")-(x-஻)=(x-w)(x2+nx-1).ᳮ%ᵨ᝞(V-(n2+l)x+n—0,*+(x-n)(j^+nx-1)=0,ᓽᨵx-஻=0ᡈ-1=0,345x-஻=06/+஻ᓈ-i=oḄᡠᨵ;<5(஻+1)x+஻=oḄ.=>⚪@52-5x+2=0ḄB.ூDᫀ௃x=2ᡈG=-I+0ᡈx=-l-I.ூ᪆௃ூᑖ᪆௃KL5MNOPB/-4x-x+2=0,RSTUᑖV(x-2)[x(x+2)-1]=0,Y3Vᑮ[\ᐵxḄ5@V.

30ூ^௃_--5x+2=0,.".x3-4x-x+2—0,.'.x(x2-4)-(x-2)=0,Ax(x+2)(x-2)-(x-2)=0,aij(x-2)lx(x+2)-l]=0,ᓽ(x-2)(/+2x-I)=0,•*.x-2=0ᡈx2+2x-1=0,Vx=2ᡈx=-1±424ᦑDᫀBx=2ᡈe=-1+0ᡈx=-1-V2.ூfg௃3⚪h⌕ὃkTᐗmn5Ḅoᵨ4⚪Ḅᐵp<᪷Y⚪rsᑮ5Ḅ.tஹD⚪47.(2021•ᔡ᪍y᧡)ᐜᓄ}4R@~(a+2)(a-2)+a(l-a),ᐸ஻=6+4.ூDᫀ௃a-4,5/5ூ᪆௃ூᑖ᪆௃✌ᐜᑭᵨ4ᓫ⚗⚗4Rᔠ⚗4ᯠK஺Ḅ~ᐭᓄ}Ḅ4ᓽD⚪.ூ^௃(a+2)(a-2)+a(l-a)=a2—4+a—a2-a-4a=+44L=q+4-4=.ூfg௃⚪ὃk᦮Ḅᔠ%4⚪Ḅᐵp<¡¢%ᵨ᦮Ḅ%ᑣ4⚪¤¥Ạ⚪§.48.(2021.©ᓭ«¬)ᐜᓄ}4R@~(x+iy+(2+x)(2-x),ᐸx=l.ூDᫀ௃2x+5,7.

31ூ᪆௃ூᑖ᪆௃ᐜ®¯ᐰஹ4R®᦮Ḅ±²4ᯠKX=1ᐭ@~ᓽV.ூ^௃L=x?+2µ+1+4-/4=2x+5.Kx=lᐭVL=2x1+5=7.ூfg௃⚪ὃk᦮Ḅᓄ}@~4¡¶¯ᐰ6<⚪ᐵp.49.(2021•¸ᓅ)º»¼½STᢇ¿»4ᵬஹÁ[»ḄSÃᑖÄB4ᐗ/ஹ10ᐗ/.ÅÆS±ᵬ»6஻Á»4ᐳÈÉQᐗ.(1)ᵨ˱4஻Ḅᦪ⊤Í஺_(2)ÎᐳÆS5x10Ïᵬ»Ð3x10'Á»4ᵨÓÔ¶ᦪ⊤Í஺Ḅ~.ூDᫀ௃(1)Q=4m+\0n(2)2=2.3xl05ூ᪆௃ூᑖ᪆௃(1)S±ᵬ»6஻Á»ᐳÈÉB2»ḄÕÃ4ᵨᓫÃᦪÖᓽ_(2)K»ḄᦪÖᐭ(1)×Ø4@4ᨬᵨÓÔ¶ᦪ⊤Í.ூ^௃(1)Q=4m+10n(2)•.•w-5xlO4,n=3xlO3.-.(2=4X5X104+10X3X103=20x104+3xl04=23xl04=2.3xIO5ᡠÛ=2.3x10$.ூfg௃⚪ὃkᑡᦪ4ÓÔ¶ᦪ4ÞḄ®4ßàḄᳮ⚪r᪷Yá▭>⚪ᑡãᦪ4ßàḄᵨÓÔ¶ᦪ⊤Íã×(<⚪Ḅᐵp.

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38da=3eS,jஹ=(3+3>=36.ூLM௃N⚪ὃPᒘ⊡º»¼ឋ¾ᔠº»2¿᦮SḄZ[ÀÁVWXYᒘ⊡º»\ÂN⚪Ḅᐵ^.57.(2022•ᗩᐶ)ÆÇ\*Èᦪᐸ¤a\ᓝÈËḄᦪÌ(1<«<9).᝞da=4eÏ⊤oḄÈᦪ\45.পÐÑজd”=1e152=225=1x2x100+25hঝda=2e252=625=2x3x100+25hঞda=3e352=1225=h(2)ÕÖ×zÙ100a(a+l)+25ᨵÛ᪵ḄᜧᐵݪÑÞßᳮᵫ.(3)ZᵨiÏ2Ù100”Ḅá(2525,f஺Ḅb.ூᫀ௃পঞ3â4100+25(2)Hwãßä᪆h(3)a=5ூ᪆௃ூᑖ᪆௃(1)ঞåæ<=জঝḄçoᵨèᨵHéêḄsᦪS⊤oᓽ3h(2)ᵫÏ2=(104+5)2=ioo«2+iooa+25,[100<3(a+D+25,îï34ᫀh(3)ᵫᖪ2Ù100aḄá(2525,ᑡ᦮ᳮ34/=25,ᑭᵨó᪷Ḅèôᓽ3.(I)জd“=1e152=225=1x2x100+25hঝda=2e252=625=2x3x100+25ঞd”=3e352=1225=3â4100+25h(2)Hwᳮᵫ᝞F•••a52=(10a+5)2=100a2+100a+25,

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46(1)ᓄAo(2)p஻r"-26=0,AḄ.ூ$ᫀ௃(1)6("+஻)o(2)6.ூ)᪆௃ூᑖ᪆௃(1)ᐜ0ᑖᔠ9u:;ᑖ)ᯠuwᑖᓄᓽ@o(2)ᐜx;yz⚗ᑭ+஻=26ᯠu᦮~Bᐭ᪷;85d2ᓽ@.ூC)௃.„,(m2rr)>j3mn(m+n](m-n)\[3mnr-,ஹ)(1)A=--------——----------L--——=j3("+஻)o

47mnm)m—nmnm—n(2)'m+n-2>j3=0,m+n=2>/3,A=V3(wz+n^=y/ix2>/3=6.ூOP௃Q⚪ὃᑖ;ᓄ120ᑖ:;ᑖ)wᑖ᪷;Ḅ85d2ᑖ;ᓄ120ᑖ:;ᑖ)wᑖ᪷;Ḅ85d2)⚪ᐵ`.64.(2020•h⁚)᝞(1),ᜧḄ☢@⊤(஺+32,¡KᜧḄ☢¢@⊤ᡂ£¤,☢£¤¥Ḅ☢¦eᓽ/+2§+஻.¡L(ᜧ)Ḅ☢ᵨ£©X¡Ḅ5ªḄ«¬®¯°±§²³´µᐰ·¸;(“+º2=/+2"+஻.x»¼½¡LḄ☢,ᵨ£©X¡Ḅ5¾Ḅ«¬¯°±§᪀À°;᪷=°;)Á¯ᐵÂ⚪”Ḅ5Ó☢5”প

48(1)ᵨÅ“☢5”,0Æ᝞(2)Ḅ☢ᐵÇ,ÈÉᑏ¾L¤Ë⚗;:;ᑖ)Ḅ°;:(2)(2)᝞(3),ZC=90°,CA=3,CB=4,CHÒÓABÓḄÕ.ᵨÅ“☢5”CHḄ¥;(3)(3)᝞(4),°ῪAABC=AC,O஺ØÓ8crÛLOOMLAB,ONLAC,CHLAB,ᚖÝᑖÞOM,N,H,àÉAO,ᵨÅ“☢5”³OM+ON=CH.(4)

49ூ$ᫀ௃(1)d+5x+6=(x+2)(x+3)o(2)yo(3)â)᪆ூ)᪆௃ூᑖ᪆௃(1)ᜧ¥Ḅ☢ãL¤Ḅ☢ä¤,¥☢¦eᓽX2+5x+6,¡Kᜧ¥Ḅ☢¢@(x+2)(x+3),ᑡ¾°æᐵÇᓽ@;(2)ᵫèéêᳮ¾AB,ᯠu᪷=S,ABc=AC.BC=gAB«CH,Bᐭᦪ)¦ᓽ@.(3)ᵫS^=S^+5,ᦋeäî☢¸;ᓽ@ª³.ABCB0ூC)௃(1)᝞(2),ᜧ¥Ḅ☢L¤,Ḅ☢ä¤,¥☢¦eᓽY+5x+6,¡Kᜧ¥Ḅ☢¢@(x+2)(x+3),ᦑ$ᫀd+5x+6=(x+2)(x+3)o(2)᝞(3)MAABCZC=90°,CA=3,CB=4,AB=>JCA2+CB2=5,S=-AC.BC=-ABXZH,“AABBCC22.…CA.CB3x412CH=------=----=—oAB55(3)᝞(4),,OM.LAB,ONLAC.CH.LAB,ᚖÝᑖÞOᵨN,H,•,SqASC=SSR஺+S^oc,.-ABCH=-ABOM+-ACON,222VAB=AC,CH=OM+ONᓽOM+QV=C஻.ூOP௃Q⚪ὃ´:;ᑖ)ḄðñòóஹḄôõöuḄ☢¯°ஹ÷ø5°)$Ḅᐵ`᪷=ijᩩúeᱯOᑭᵨôõöuḄ☢¯°0Æᑖ᪆ஹüᳮe12.65.(2020•ýþᗩᐶ)/+12xḄᜧ.(1)(ᵨ“<”"="ᡈ">'’)

50জx=lஹ/+12xঝx=0x2+12xঞx=-2x2+\2x.(2)!"#x$%&'ᦪN+12xᨵ*᪵Ḅᜧᐵ-./0ᳮᵫ.ூ4ᫀ௃(1)জ7ঝு9ঞு9(2)x2+\>2x,ᳮᵫ:;᪆ூ;᪆௃ூᑖ᪆௃(1)᪷?@ᦪABCDE@ᦪAḄC᪷?ᨵᳮᦪḄᜧDE4ᫀ9(2)᪷?FᐰHIJADE4ᫀ.ூK;௃;(1)জx=lx2+l=2xঝx=0x2+l>2xঞx=-2x2+l>2x.ᦑ4ᫀM—;>;>.(2)x2+\>2x.P0:''x2+]-2x=(x-1)2>0,.,.^+\>2x.ூRS௃T⚪ὃWXB@ᦪAḄCᨵᳮᦪḄᜧYZ᦮Aᜧ\P0JA]^Aᑖ;ஹ_Fᐰ!"];⚪ᐵ`aᳮ;᪷?“A-B”Ḅbc“AஹB”Ḅᜧ.66.(2020•effg)᝞i“jk”lmnᜓᵨ50mḄpqrᡂ7ᙽ☠ᜋḄwxyz{wxyzḄ|Ma[,n),lmb(m).ᜋ7777777771(1)஻=20B~ḄC9(2)mᙢᩩḄ▲ᑴ஺Ḅ$CrM184a426,BᓃḄ$Cr.ூ4ᫀ௃(1)b=159(2)12

51ூ;᪆௃ூᑖ᪆௃(1)᪷?ᐵ-“rqḄ|M50”Dᑡ@ᦪAa=20@ᐭᡠᑡABbḄC9(2)ᵫ(1)DEa,bḄᐵ-AᵨᨵbḄA⊤&¡ᔠ18<஺<26,ᑡᐵ¥bḄ_A¦§Ḽ_A¦ᓽDBbḄ$Cr.ூK;௃;(1)ᵫ⚪&Ea+M=50,4=2(®20+2/?=5().;E6=15.(2)V1818••150-2X26;´Z_A¦E1246416.4wxyzµḄ$CrM124¶416.ூRS௃·⚪¸⌕ὃWXᑡ@ᦪAº»ᳮ;⚪&Eᐵ-Aa;⚪ᐵ`.¼ὃWX;_A¦½_ᜧ.67.(2020¿À)ᙠᦪḄÂÃÄÅᡃÇÈÉÊᐸ7ÌᐹᨵÎÏᱯឋḄᦪᐙÓÔ᜻᝞ÂÃÖᯠᦪᡃÇØÙ7ÏᱯÚḄÖᯠᦪ——“Ôᦪ”.ÛÜÊ¥ÝÞÖᯠᦪ஻ᔜÞᦪàá_M0,âãÞᦪàᓝÞᦪàåាÔçèZÞᦪà᦮◀ᑣë´ZÖᯠᦪ஻M“Ôᦪ”.ì᝞426a“Ôᦪ”^M4,2,6á_M0,â4+2=6,6çè6᦮◀9643_a“Ôᦪ”,^M6+4=10,10_çè3᦮◀.(1)ᑨï312,675aᔲa“Ôᦪ”./0ᳮᵫ;(2)BãÞᦪàᓝÞᦪàᜧ5Ḅᡠᨵ“Ôᦪ”ḄZᦪ/0ᳮᵫ.ூ4ᫀ௃(1)312a“Ôᦪ”675_a“Ôᦪ”ᳮᵫ:;᪆(2)611,617,721,723,729,831,941.ᳮᵫ:;᪆.ூ;᪆௃ூᑖ᪆௃(1)᪷?“Ôᦪ”ḄÛÜòóᑨïᓽD9(2){ᓝÞᦪàMx,ZÞᦪàMy,ᑣãÞᦪàM(x+5).᪷?⚪&ᑨïxஹy$C᪷?“Ôᦪ”ÛÜ

52⌲7ᑨïᓽD.ூK;௃÷1øV3,1,2á_M0,â3+1=4,4çè2᦮◀...3_a“Ôᦪ”.V6,7,5á_M0,â6+7=13,13_çè5᦮◀ù675_a“Ôᦪ”9÷2ø{ᓝÞᦪàMx,ZÞᦪàMy,ᑣãÞᦪàM÷x+5ø.ᐸx,yáaº᦮ᦪâ12,úû9.ᓝÞᦪàZÞᦪàḄåM2x+5.ᡝ12r+5=7,·y=lᡈ7,“Ôᦪ”ᨵ611,617ÿ2
2r+5=9,
y=lᡈ3ᡈ9,“ᦪ”ᨵ721,723,729x=3
,2x+5=ll,
1,“ᦪ”ᨵ831ᡝ4
2x+5=13,
y=l,“ᦪ”ᨵ:941ᡠ!ᦪ"#ᓝ!ᦪ"ᜧ5Ḅᡠᨵ“ᦪ''Ḅ(ᦪ)7.ூ,-௃/⚪1“234”5⚪ᳮ7“234”8᪷:;ᨵᦪ<=>?◚AᩩCDEᑖ᪆Hᓄ1ᡠ<ᦪ<5⚪)7⚪ᐵK.68.M2022•PQRST▅Vᩞᧇhcᩞᧇ1YᐵZXḄ\ᐗ^_`aa/+bx+c=0Mf0TḄg(᪷1X/,X2,ᑣᑴ+j2=-\/XIX2=-aaᩞᧇ2:;=\ᐗ^_`a12—x—1=0Ḅg(mᦪ᪷ᑖn1opqm2஻+t஻2Ḅu.7•,\ᐗ^_`a/\%—1=0Ḅg(mᦪ᪷ᑖn1஻7,/./w+n=1,mn=-1,ᑣy2஻+y/=t஻M6+zT=—1x1=—1᪷:{|ᩞᧇ}ᔠᡠ<Ḅ=>ᡂᑡ5⚪M1Tᩞᧇᳮ7\ᐗ^_`a2%2—3%—1=0Ḅg(᪷1X/,X2,ᑣᑍ/+&=X1X2=.ফ#ᵨ;=\ᐗ^_`a2%2-3x-l=0Ḅg᪷ᑖn1“ஹ஻q+Ḅu.mnM3T;=mᦪsஹf12—3s—1=0,2F—3f—1=0,sq1-1Ḅu.st31ூᫀ௃M1T;:--22বᡈ-p

53ூ7᪆௃ூᑖ᪆௃(1)᪷:\ᐗ^_`a᪷ᦪḄᐵ¡DE¢£ᓽ¥31F?ni(2)᪷:᪷ᦪḄᐵᐜq§nin=#ᯠ2+'DE©ªq7ᓽ¥f22mn3111(3)᪷:᪷ᦪḄᐵᐜq§s+f=94=-ᯠq§MḄuᯠ¬,DE©ªq7ᓽ¥.225t(1)7,\ᐗ^_`aᓅ4ᱏ1=0Ḅg(᪷1ᑴX2,.஺\33c1°+j2=\=\_Dx\/x2=-=-7,a22a231ᦑᫀ1³;\.22(2)•\ᐗ^_`a´341=0Ḅg᪷ᑖn1yஹ஻.b-33c1..m+n=——=-----=—,mn=—=——,a22a222.nmm+n••—i—=------mnmn+-2mnmn2_23~~~2(3).•mᦪsஹ2s2-3S-1=0,2-1=0,f¥µ¶`a2N-3x-l=0Ḅg(᪷,^-33cls+f=—=---=—,st=-=—,a22a2•:(r-5)2=(r+5)2-4st

54=—F2417=—4..t-s=---ᡈ-5=-----,22qߟ=¹
---=—=^-=-Vn,2ststf-s=-¹
=—2-=Vn,2stst£s5¼{ᑖ᪆¥=Ḅu1J¾ᡈ-J¾.stூ,-௃/⚪¿⌕ὃÂÃ\ᐗ^_`a᪷ᦪḄᐵᐰÅ`ÆÇḄ©ª¢£᪷:᪷ᦪḄᐵq§-S=qᡈt-s=-q,)7/⚪ḄᐵK.2269.(2022ÈÉ)Y\(P!ᦪMḄ(!ᦪ"ᓝ!ᦪ"ḄÅ`?ា)“Ìᣵ(!ᓝ!ᦪ"ÎᑮḄg!ᦪᑣÐ(P!ᦪM1“ÑÒ?ᦪ”.Ó᝞M=2543,3?+4?=25•,•2543)“ÑÒ?ᦪ”Ö᝞M=4325,V52+22=2929x43,.4325×)“ÑÒ?ᦪ”.(1)ᑨÙ2022,5055)ᔲ)“ÑÒ?ᦪ”8ÛÜᳮᵫz»-4-z/(2)\(“ÑÒ?ᦪ”MḄᓟ!ᦪ"1஺!ᦪ"1b,ᓝ!ᦪ"1c,(!ᦪ"1d,àG(M)=â9,P(M)äl0(”1+eåæG(M),P(M)ᙳ)᦮ᦪ
q§ᡠᨵᩩCḄூᫀ௃প2022×)“ÑÒ?ᦪ”,5055)“ÑÒ?ᦪ”;ᳮᵫê7᪆(2)8109ᡈ8190ᡈ4536ᡈ4563.ூ7᪆௃ூᑖ᪆௃(1)᪷:“ÑÒ?ᦪ”Ḅ34DEëìᓽ¥;(2)ᵫ“ÑÒ?ᦪ”Ḅ34¥Î10a+b=c2+d2,᪷:G(M),P(ᔊ)ᙳ)᦮ᦪ¥Î஺+1=9,,2+/=81-2”13Ḅîᦪ:ΧïᔠᩩCḄc,"Ḅuᯠᓽ¥ñ3§প

5572022×)“ÑÒ?ᦪ”,5055)“ÑÒ?ᦪ”;ᳮᵫV22+22=8,8/20,•••1022×)“ÑÒ?ᦪ”;:52+52=50..♦.5055)“ÑÒ?ᦪ”;(2)M1“ÑÒ?ᦪ”^l0a+b=c2+d2,A0Ḅüý7⚪ᐵK)⌕ᳮ7234ü᪷:ᩩCþ§ᔠ〉Ḅ“ᦪ”.

56