2021-2022学年广西南宁市八年级（下）期末数学试卷（附答案详解）

《2021-2022学年广西南宁市八年级（下）期末数学试卷（附答案详解）》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

2021-2022
ᓭ
ᦪᔁ1.ᑡᨬ᪷ḄA.V3B.V8C.713D.V42.*+,y=-2x+lᔣ45637ᓫ9:;<ᡠ>+,Ḅ?᪆A.y=-2x—2B.y=-2x+4C.y=—2x—3D.y=—2x+33.ᑡ4AᦪBCDᦪḄA.1,2,3B.2,3,4C.3,4,5D.6,7,84.ᑡᔜGHIJḄA.V2+V3=V5B.2A/3-5V3=-3C.V2+V32=5D.V2+V2=2V25.ᑡLMIJḄA.OAPQ5RSOAPQTUḄVQW5RVQWB.PX,TUḄ5RVQWYWC.Z7X[+XḄVQW\WD.OA]QTUḄ5RVQWI^W6._ᱯaPbc⌱e“ghi”kRlmnoᨬ<ᵫᵬஹstuᡊwxᐭzot{ᔜl☰10~HᵬஹstuᡊwḄᡂ[99.68ᵬḄ^0.28,sḄ^0.21,ᑣᑡLMIJḄA.ᵬḄᡂnsḄᡂB.sḄᡂnᵬḄᡂC.ᵬஹst{ᡂḄឋTD.MJḄᡂ7.᝞oABCZAB=4,BC=6,ACḄᚖ+5ᑖ,ADஹE,ᑣACOEḄᕜ:A.6B.8C.10D.128.k>0,b<0,ᑣOᦪy=kx+bḄᜧ¡b

19.᝞YWABCDḄPX,:ᑖ¢b6£8,¤PPX,AC4¦§O¤¨©¤A,CªᔠPE஻BCAB
E,PF//CDADᓟF,ᑣ▢®ᑖḄ☢°A.12B.11C.10D.2410.᝞+,y=2%©y=²+bT³´¤Pm,2,ᑣᐵ´xḄ^·kx+b=2Ḅ?A.x=-B.x=1C.x=2D.%=4211.¸¹ºH»¼½¾c¿᪵ḄÁ⚪ÃÄÅÆஹÇÅÈᐳª20ᓟËÆÌȪÍᣚᐸOÅាÑO᪵ª.ÒÃÓÅÆஹÈ5ᙳᔜªÕÖᓟË×ØÓOÅÆ5ᙳªxᓟËÓOÅÈ5ᙳªyᓟË᪷B⚪§ÙᑡÚ^·Ab()A(5%+6y=20g(5x+6y=20,(5%-y=6y—x'(5x+y=6y+%C(5%+6y=20ß(6%+5y=20>14x+y=5y+%>(4%—y=5y—x12.᝞¤E/ᙠYWḄPX,AC4s4DC=120°,஽BEC=CBF=50°,E£>©BFḄæ:,³´¤M.ᑣP´èéê:জ4BME=30°íঝï4DEðï4BEíঞEM=BCíটAE+BM=gEM.ᐸIJéêḄ7ᦪ()A.17B.27C.37D.4713.⌕ôRZᨵ§öᑣxḄ÷ø.ù2⚓ᐳ18⚓

214._ûüýþᡂÿᑖ
100ᑖᢥ᜜ᡂஹᡂஹᡂ235Ḅᡂ.⚗ᡂ
90ᑖஹ90ᑖஹ80ᑖᑣḄᡂᑖ.15."#ᦪy=2x-lḄ%&'y(Ḅ)*ᙶ᪗
.16.᝞%.ᡃ012ᦪ℉456789Ḅ":;⚪"᪷>?@1AᢚCD>?⚔FGᙠI>?JF3KᜐᢚCᜐIᙢ☢Ḅ@OK(1A=10K).18.᝞%ᙠR☢STᙶ᪗USV/
XY#ᦪy=xḄ%&*4Ḅᙶ᪗
(1,0),Z*44X(ḄᚖV)SV/\*஺1^4D1
_4X`a
B1C1D1bZ*G4SV/ḄᚖVᚖc
&)X(\*
^e

_4X`a2c2஺2Z*4X(ḄᚖVᚖc
f)SV/\*஺3^f஺3
_4X`a4383c3஺3,…ᢥghij4k"ᡠmᑮḄX`ao2022B202202022஺2022Ḅ☢p-19.V2x(1+V2)+>/4-V6V3.20.ᐜᓄtuvwx(x+1)4-(x+l)(x-1)-x,ᐸx=21.
y"z{|■◫fញ◅ᦗᦗo᪥ஹᔜ200fy“■◫”(ᑖ100ᑖ),¢ᑖ£ᙠஹᔜ¤¥¦§10fḄᡂx(ᓫ©ᑖ)yªஹ᦮ᳮ᝞

3:86,90,79,84,74,93,76,81,90,87.:85,76,90,81,84,92,81,84,83,84ᡂ⚣ᦪª⊤70b=,c=.(2)h¿ᑖᦪÀÁ\85ᑖÂ
“ÃÄ”Å.Æ:ᡂÇᑮ“ÃÄ”ḄfÈᦪ.(3)ÉÊ
Ë:ḄfÌÍ■◫ḄÎÏRÐÑÒÓÔᳮᵫ.22.Ö×ῪTaABCḄJ_BC=20cm,஺ῪAB¸"*ÙCD=16cm,BD=12cm.(1)vÚCD1ABb(2)vÛTaḄῪḄÜO.23.᝞%ᙠnABCDÖoB>BC.(1)ÝÞ'j44N40CḄRᑖV)AB\*E,ᙠ0c¸ß§OF=AD,àáEF!(⌕vKh4%ãᶇ4%åæÀᑏ4è)(2)éêëÚéêì_aAEFDḄaíëîïÚ.24.ᙠyð᪷ñᓄtòᡃóᨵòõö¸᝞@÷"᪵Ḅñ?.᪵Ḅñ?ᡃóù^úᐸy"zᓄtû=^=îýþ=ÿ/=r-1ᓄḄᑖᨵᳮᓄᑭᵨᑖᨵᳮᓄᑡ⚪4⚓ᐳ18⚓

42(1)ᓄ:(2)%஺'(Ḅ)ᦪ+ᑖ,?Ḅ./(3)01Ḅ☢3435+1,67849-2,,:Ḅᕜ8.25.=ᖪ?├AAஹ8CDEḄᡭᓺH├A5IADJ10I8DᡭᓺHḄᑭKJ42000ᐗ,├A10IADJ5I8DᡭᓺHḄᑭKJ41600ᐗ.(1),NIADJBDᡭᓺHḄ├AᑭK/(2)ᖪ?OᑜQRAஹ8CDEḄᡭᓺHᐳ100IᐸTADᡭᓺHᦪUVWX8DᡭᓺHᦪUḄ6YZQRADᡭᓺH஺I100IᡭᓺHḄ├A[ᑭK4wᐗ,\ᖪ?QRAஹBCDEḄᡭᓺHᔜ^WI_`a├A[ᑭKᨬᜧd(3)ᙠ(2)Ḅᩩgᔆi4jkᖪilmnᑭoADᡭᓺHḄpᔆqrmᐗ(0

5ᫀJ᪆1.ூᫀ௃Aூ᪆௃V5'ᨬ᪷Aᔠ⚪/V8=2V2,8Vᔠ⚪/=CVᔠ⚪/V4=2,஺Vᔠ⚪/ᦑ⌱4᪷ᨬ᪷Ḅᭆ¢£⌱⚗⌲6ᑖ᪆ᓽ§.¨⚪ὃªjᨬ᪷Ḅᭆ¢⚪ᐵ«ᙠX¬\u®.2.ூᫀ௃Bூ᪆௃ᵫ⚪°±²Ḅ᪆4y=-2X+1+3,ᓽy=-2x+4.ᦑ⌱B.᪷y³=/^+ᓃ±ᡃ.Vx¸ᨵb¹ºᦋxᓽ§.¨⚪ὃªḄ'6¼ᦪḄ½¾¿Àxᣚ¬Â“ÃÄ”ḄÆᑣ'È⚪Ḅᐵ«.3.ூᫀ௃Cூ᪆௃A.l2+22^32,ÉÈV'ÊËᦪᦑÈ⌱⚗Vᔠ⚪/B.22+32*42,ÉÈV'ÊËᦪᦑÈ⌱⚗Vᔠ⚪/C.32+42=52,ÉÈ'ÊËᦪᦑÈ⌱⚗ᔠ⚪£>.62+72^82,ÉÈV'ÊËᦪᦑÈ⌱⚗Vᔠ⚪/ᦑ⌱C.ᑭᵨÊËᦪu®Rᑖ᪆ᓽ§.È⚪Ì⌕ὃªjÊËᦪᐵ«'ÎÏÐÑ+᮱=஺2ḄÓÔÕ᦮ᦪ×4ÊËᦪ.4.ூᫀ௃Dூ᪆௃4ᡈJᡃV'ÙÚ᪷V`ᔠÛ⌱⚗4Vᔠ⚪/B.2V3-5V3=(2-5)V3=-3V3,⌱⚗BVᔠ⚪/C.(V2+V3)2=2+276+3=5+276,⌱⚗CVᔠ⚪/D.>/2+&=(1+1)V2=2VL⌱⚗Dᔠ⚪/ᦑ⌱D.᪷᪷ḄឋÝÙÚ᪷Ḅu®Þᐰà᪷ḄÃÄᑣᓽ§°pᫀ.6⚓ᐳ18⚓

6¨⚪Ì⌕ὃª᪷ḄÃÄÞᐰàÙÚ᪷Ḅu®.5.ூᫀ௃Cூ᪆௃Aஹ6á£7â6á£7ãḄ~71'~71ᡠA⌱⚗┯æVᔠ⚪/8ஹ£çèéḄ~71'01ᡠ8⌱⚗┯æVᔠ⚪/CஹÓÔçê'yçḄ~71'01ᡠC⌱Õë/ᔠ⚪/஺ஹ6áì7èéḄ~71'Õ1ᡠ஺⌱⚗┯æVᔠ⚪.ᦑ⌱C.᪷~71Ḅᑨu£ARᑨî/᪷ï1Ḅᑨu£BRᑨî/᪷01Ḅᑨu£CRᑨî/᪷Õ1Ḅᑨu£஺Rᑨî.¨⚪ὃªjÕ1Ḅᑨu01Ḅᑨuï1Ḅᑨu~71Ḅᑨu⚪Ḅᐵ«'jᨵᐵḄᑨuuᳮðñVᜧ.6.ூᫀ௃Bூ᪆௃•••ᵬḄô'0.28,Ḅô'0.21,•Ḅᡂö÷ᵬḄᡂöøu/ᦑ⌱B.᪷ôḄ®§pᑨî.ô'ᵨᩭ⊝U6áᦪûüᜧ)ḄUôý)⊤ÿ
ᦪᑖᔜᦪᙳᦪᓽᦪ.⚪ὃḄ!ᵨᩭ⊝%&
ᦪᜧḄ%ᜧ⊤)
ᦪᙳᦪᜧᓽᜧᦪ*+,-⊤)
ᦪᑖᔜᦪᙳᦪᓽᦪ.7.ூ0ᫀ௃Cூ3᪆௃35•.•789A5CD!:789•DC=AB=4,AD=BC=6,••ACḄᚖ<ᑖ=>AD?@E,AE=CE,•••CDEḄᕜB=DE+CE+DC=DE+AE+DC=AD+DC=6+4=10!ᦑ⌱5C.ᵫ:789ḄឋHIJDC=AB=4,AD=BC=6,ᵫ=Kᚖ<ᑖ=ḄឋHIJAE=CE,IJCDEḄᕜB=4D+DC,ᓽLIJMN.⚪ὃO:789ḄឋHஹ=Kᚖ<ᑖ=ḄឋHஹQR9ᕜBḄST+UVWX

7:789ḄឋHYZ[:\ᳮST!3^_⚪Ḅᐵa.8.ூ0ᫀ௃Bூ3᪆௃351.•k>0,b&cdᦪy=kx-bḄefghᑮj!kᓣḄ■■■b<0,&cdᦪஹ=kx+bḄef>?ymḄnomᦑ⌱5B.᪷ᨌbḄrst<=ḄuᓄwxyzymḄ>@Ḅ{|ᓽL.⚪ὃO&cdᦪḄefz}ᦪḄᐵ}3⚪Ḅᐵa!O3}ᦪzef{|Ḅᐵ},*ᜧ.9.ூ0ᫀ௃Aூ3᪆௃35APzEF>?஺@.•••789ABCO9•••BC//AD,AB//CD.•)PE//BC,PF//CD,PE//AF,PF//AE.b789AEPF!:789.SAPOF=SAAOEb▢ᑖḄ☢!BCḄ☢•••BCḄ☢=9Ḅ☢=|x(|x6x8)=12,ᑣ▢ᑖḄ☢!12.ᦑ⌱5A.)789AEPF!:789APzEF>?஺@ᑣAPOFḄ☢?aAOEḄ☢.ᡠ▢ᑖḄ☢?9☢Ḅ&o.⚪ὃO9ḄឋH3^⚪Ḅᐵa!IJ▢ᑖḄ☢!4BCḄ☢.10.ூ0ᫀ௃Bூ3᪆௃35,<=y=2xzy=kx+b>?@P(m,2),•••2=2m,■■m=1,•••P(l,2),8⚓ᐳ18⚓

8bx=1y=kx+b=2,bᐵ?xḄkx+b=2Ḅ3!x=1,ᦑ⌱5B.✌ᐜᑭᵨdᦪ3᪆y=2xJḄᯠ¢£᪷¤dᦪefḄ>@¥ᙶ᪗!ᐵ?xḄkx+b=2Ḅ3LI0ᫀ.¨⚪©⌕ὃO&cdᦪz&ᐗ&cᐵa!I¤dᦪefḄ>@ᙶ᪗.11.ூ0ᫀ௃Cூ3᪆௃35ᵫ⚪ICM+/ᦑ⌱5C.᪷“®¯ஹ°®±ᐳ²20ᓟ´¯µ±²¶ᣚᐸ&®ាº&᪵²”ᑡ
ᓽL.⚪ὃOᨵ¿▭_⚪ÁfJbᐗ&c
30⚪Ḅᐵa!ÂÃ⚪JÄÅᦪÆJᔠ〉Ḅ%ᐵ}ᑡ
.12.ூ0ᫀ௃Dூ3᪆௃35•.•789ABO!9^ADC=120°,•••AD—AB-BC-CD,/.BAD=BCD=60°,/.DAE=BAE,Z.DCE=BCE=-/.BCD=30°,2vBFE=BCE+Z.CBF=30°4-50°=80°,EBF=180°&BEC-BFE=180°—50°-880°=50°,ᙠCDEyCBECD=CBZ-DCE=BCE*CE=CE.MCDEdCBE(SAS),•DEC=BEC=50°,•BEM=DEC+BEC=100°,BME=180°-BEM-(EBF=180°—100°—50°=30°,ᦑজËt+ᙠ4DEyABE(AD=AB\z-DAE=BAE,\AE=AE•ᦑঝËt+•EBC=Z.EBF+CBF=100°,•BEM=EBC,Mᙠ485y4E8C“B

9(Z.BEM=Z.EBC1/.BME=(ECB=30°,VBE=EB•••BEMaEBC(AAS),:BM=EC,EM=BC,ᦑঞËt+ÎÏ>AC?O,᝞eᡠÑ5,,789ABCD!9;OA=OC,AC1BD,vZ-DCO=30°,OD=\CD=^BC,OC=60D,OC=—BC,2.AC=2OC=\[3BC,■■BM=EC,EM=BC,.AE+BM=AE+EC=AC=+BC=,EM,ᦑটËtËtMÓḄÔᦪ!4Ôᦑ⌱5D.ᐜᵫ9ḄឋHI40=4B=BC=CD,ABAD=/.BCD=60°,^DAE=ABAE,LDCE=^BCE=30°,£ᵫQR9Ḅ᜜RឋHI4BFE=80஺ᑣ/EBF=50°,ᯠ¢CBE(SAS),INDEC=-BEC=50",[ÖIJজËt+ᵫ&454ADE^LABE,IঝËt+JEBC(44S),.BM=EC,EM=BC,ঞËt+ÎÏ8஺>AC?O,ᵫ9ḄឋHI4c1BD,£ᵫ3ூ3᪆௃35ᵫ⚪Ix-3>0,3Ix>3,ᦑ0ᫀ5x>3.᪷bc᪷ᨵḄᩩÞᑡJ*3*ᓽL.⚪ὃḄ!bc᪷ᨵḄᩩÞWXbc᪷Ḅßàᦪáâ!ãn.14.ூ0ᫀ௃85ூ3᪆௃3590x^M+90xᵫ+8°x▭85ᑖä,ᦑ0ᫀ585.᪷åᩗᙳᦪḄSTç[:STᓽL.10⚓ᐳ18⚓

10⚪ὃåᩗᙳᦪḄySTçᳮ3åᩗᙳᦪḄWXåᩗᙳᦪḄSTç!Ët30Ḅèé.15.ூ0ᫀ௃(0,-1)ூ3᪆௃35x=0,ᑣy=-1,ᦑ&cdᦪy=2x-1ḄefzymḄ>@ᙶ᪗5ᦑ0ᫀ5<Ïᑭᵨ&cdᦪzym>ᑣò=0[ÖIJ0ᫀ.¨⚪©⌕ὃO&cdᦪefk@Ḅᙶ᪗ᱯôËtõö¥÷ᙶ᪗ᐵ}!3⚪ᐵa.16.ூ0ᫀ௃4.55ூ3᪆௃35úûᢚýᜐᙢ☢xᑣ(10-x)᪷ᳮ:X2+32=(10-X)2.x=4.55,ᢚᜐ!ᙢ☢Ḅ$%4.55.ᦑᫀ4.55.()ᢚ*+,᪀ᡂ/012134()ᢚᜐ!ᙢ☢xᑣ(10-x)ᑭᵨᳮ⚪ᓽ9.:⚪ὃ<=ᳮḄ>ᵨ⚪Ḅᐵ@Aᑭᵨ⚪BCD᪀⌼01213FGHᵨᳮ⚪.10ᡠ17.ூᫀ௃3ூ᪆௃᝞OPQRPCTᔠVᢚWEFᨬᜧᵫ]ᢚḄឋ_BC=B'C=10cm,ᙠRt3bB'D=yIB'C2-CD2=V102-62=8cm,••ABr=AD-BfD=10-8=2cm,4=ᑣ==AE=AB—BE=6—%,ᙠRXMEbAE2-^-AB*2=B'E2,ᓽ(6—x)2+22=x2fm=/^Rt^BEF^P*EF=\!BC2+BE2=J102+(y)2=^^cm.rERATᔠVEQḄᨬᜧt6vL

116ᓅᵨPᙠ}ᑨᢚWEQᨬᜧḄᑭᵨᳮᑡ8EḄO330.18.ூᫀ௃(1021ூ᪆௃•••0/¡ᦪy=xḄOz.DOA=45°,11ᙠ3481cl%b,£4ἔ=90஺,1:.Z-ODA=45°,11P&Ḅᙶ᪗(1,0),:.OA=1,X:.஺〈1=OA=1,13AiBiGAḄ☢ª=1,᪷ᳮ஺஺1=>DA=y,X2AB=AO=«22234282c2஺2Ḅ☢ª=¬ᳮ943஺3=஺3=34383c3஺3Ḅ☢ª=(1)2)®342022B2022c2022஺2022Ḅ☢ª=(~)2021>ᦑᫀ¯2஺21.᪷3Ḅឋ_°±/²¡ᦪḄ᪆9=45஺FG93&B1GO1Ḅ3A1B1G5Ḅ☢ª᪷ᳮ934282c2஺2Ḅ34282c2஺2Ḅ☢ª¬ᳮ934383c3஺3Ḅ☢ª³ᐸbḄµ¶ᓽ9342022B2022c2022஺2022Ḅ☢ª.⚪ὃ<=3Ḅឋ_/²¡ᦪOPḄᙶ᪗ᱯ¸³☢ª¹ºḄµ¶A⚪Ḅᐵ@.»12⚓ᐳ18⚓

1219.ூᫀ௃V2x(l+V2)+V4-V6-V3=V2+2+2-V2=4.ூ᪆௃ᐜ®²᪷Ḅ¿◀ÁÂÃÁᓽ9.⚪ὃ<=®²᪷ḄÄᔠHÅÆÇÈᙢÉÊA⚪Ḅᐵ@.20.ூᫀ௃x(x+l)+(x+l)(x-l)-x=x2+x+x2—1—X=2x2-1,rx=ËVÌ=2x(V3)2-1=2x3—1=5.ூ᪆௃ᐜÍÎÏᔠ¬Ð⚗ᯠ*ÒXḄtÓᐭᓄÖ*Ḅ)ÉÊᓽ9.⚪ὃ<=᦮ḄÄᔠH-ᓄØtÅÆÇÈᙢÉÊA⚪Ḅᐵ@.21.ூᫀ௃28584ூ᪆௃(I)ஹ•ÚÛÜḄ10ÝÞßbᨵ8ÝÞßᡂàá}90ᑖa=10-7—1=2,᪷ãᦪḄä9åc=84,ÒæÛÜ10ÝÞßḄçèᡂà᣸,êë74,76,79,81,84,86,87,90,90,93,᪷bìᦪḄä9åíîᦪḄbìᦪb=ï=85,ᦑᫀ2,85,84ð(2)æÛÜ10ÝÞßḄᡂàbñá}85ᑖḄᡠᓰó=I*ÚÛÜ10ÝÞßḄᡂàbñá}85ᑖḄᡠᓰ஺æÛÜçèᡂàôᑮ“÷ø”ḄÞßᦪ200X=100()ÚÛÜçèᡂàôᑮ“÷ø”ḄÞßᦪ200x2=60()®æஹÚÛÜçèᡂàôᑮ“÷ø”ḄÞßᦪᑖú100û60ð(3)•••æஹÚÛÜçèᡂàḄüᙳᦪþ~ÚÛÜçèᡂàḄÿ
ᡂḄḄ■◫Ḅ.(1)"⚪$%&'Ḅ%ᔜ)*+,10-Ḅᡂ%./01'a,cḄ2᪷4%5ᦪ78.1'8:(2)ᑖ:1'ஹ<=Ḅ>?@ABCᦪᓽ.E(3)FGᦪ4ḄᙳᦪIJKLḄᜧ/0>ᓽ..

13O⚪P⌕ὃSTᦪU⚪ḄᐵWXᙳᦪஹ%5ᦪஹTᦪY᩽Ḅᭆ\.22.ூ^ᫀ௃Ua(1)BC=20cm,CD=16cm,BD=12cm,.•cd+c/)2=BC2,᪷4ef7ᳮ⌮7ᳮ.^BDC=90°,ᓽCOB(2)iῪklxcm,ᑣn஺=(x-12)cm,ᵫ(1).+2=c2,CD71ᓽa0—12r+162=x2,Utu=vῪklvcm.ூU᪆௃O⚪P⌕ὃSxef7ᳮḄ⌮7ᳮ᝞z{|}Ḅ{~ka,b,ccda?+/=஺2,{|}X/|{|}.(1)4ef7ᳮḄ⌮7ᳮᓽ.tᑮ/BDC=90஺ᓽ.tᑮCD1AB-,ফiῪklmn,ᑣ40=(x-12)cm,ᵫপ.n஺2+c02="2,U஺12/+162=/,ᓽ.tᑮῪk.23.ூ^ᫀ௃Ua(1)᝞AEQFlᡠ;(2)a~}AEF஺X}.a•••~}ABCCl~},.•■AB//DC,Z.CDE=/.DEA,■■DEᑖN/WC,•••-CDE=Z.ADE,•••Z.ADE-Z.DEA,•••AD=AE,XvAD=DF,•••DF=AEB.DF//AE,~}AEFDX~}AD=DF,•.□4EF஺X}.14⚓ᐳ18⚓

14ூU᪆௃প|ᑖOEᑖ4DC,ᯠ,DF=4D2
ᐜᑭᵨ~}AEFOX~}ᯠᑭᵨAO=OF.ᑨ£wlEFOX}.O⚪ὃSx¤ᩖa¤ᩖXᙠ§¨©OḄ©Ạ«¬X®ᔠx°±}Ḅឋ³©O´.Uµ¶·⚪$ḄᐵWX¸៉©O°±}Ḅឋ³®ᔠ°±}Ḅ©Oឋ³º¤ᩖ»Uᡂ©O⌲½¾.¿ὃSx}Ḅᑨ7.24ூ᝞À௃U.প2__2.-b
__2ÁS_A64•1Ãᐭ1U.প5/5ÅK+8
ÅÆ—2—VbV3ফaXÈḄᦪÉᑖ•••a=V2—1,3_3_3(e+1)=3(724-1)=372+3a-V2-1-(V2-1)(V2+1)3
,,,Ê}Ḅ☢Ìl3Í+1,~klΗ2,Ê}ḄÏ~klaB=ÐÑ=15+66+Á+2=17+7ÒÓÊ}Ḅᕜkla(17+7V5+V5-2)x2=30+16Í,^aÕḄᕜkX30+16Ö.ூU᪆௃1
᪷4⚪$%Ḅ?×.BU^O⚪E2
᪷4⚪Ø.BÙ.B1tᡠ1Ú×Ḅ2E3
᪷4⚪Ø.B1tÊ}ḄÏ~k"Á.B1tÓÊ}Ḅᕜk.O⚪ὃSÛÜÝᳮᦪḄᜧஹÞ᪷ÚḄßᔠàÜஹÞ᪷ÚḄáᵨU^O⚪ḄᐵWXâÕãᔜäḄåÜ´.25.ூ^ᫀ௃Ua1
iæçAèᡭᓺ*ḄᑭëlxᐗæçBèᡭᓺ*Ḅᑭëlyᐗ,5x+10y=2000᪷4⚪Øt:10x+5y=1600'x=80Ut:y=160'•••æçAèᡭᓺ*Ḅᑭël80ᐗæçBèᡭᓺ*Ḅᑭël160ᐗ.^:æçAèᡭᓺ*Ḅᑭël80ᐗ,æçBèᡭᓺ*Ḅᑭël160ᐗ.(2)ᵫ⚪Øtaw=80a+(100-a)X160=-80a+16000,v-80<0,w)஺ḄîᜧÁ,ஹ100-avïஹ100va>----------ᓽa>—23•aXð᦮ᦪ•••a—34òóᨬᜧ,•••100-a=66çÆ••õᖪ÷ø¬AèùḄᡭᓺ*34çBèùḄᡭᓺ*66çòúûü├þᑭëᨬᜧ.^aõᖪ÷ø¬AèùḄᡭᓺ*34çBèùḄᡭᓺ*66çòúûü├þᑭëᨬ

15ᜧ.(3)ᵫ⚪w=(80+m)a+(100—a)X160=(m-80)a4-16000,100”mv—0ஹᓽm>80!஻Ḅ$ᜧ&$ᜧ•.Q=50wᨬᜧ)ᓃ100—Q=50(+)ঝ-.80<0ᓽTH<80!aḄ$ᜧ&01.•.a=34wᨬᜧ4100—a=66(+)ঞTH—80=0ᓽm=80w=16000,.஺78—WaW50Ḅ᦮ᦪwᨬᜧ.<=ᡠ?ᖪA├CD100+ᡭᓺGHᑭJᨬᜧḄKLMᫀOAQRBQᡭᓺGTKL50+.ூV᪆௃(1)YZ+AQᡭᓺGḄᑭJOxᐗZ+BQᡭᓺGḄᑭJOyᐗᵫ⚪ᑡ_xஹyḄ`ᐗ.aMbcdVᓽef(2)ᵫHᑭJhijkQlᡭᓺGᑭJmRᑡ_ᑭJwᐵiaḄoᦪV᪆p᪷roᦪḄ$0ឋtuᑭJḄᨬᜧvᓽef(3)ᐜᵫ⚪ᑡ_ᑭJᐵiaḄoᦪᐵxpᯠzᑖ.a⚗xᦪᜧi0ஹhi0ஹ1i0}k~ᓽe.⚪ὃ.aoᦪR`ᐗ.aMbcḄᵨᐵ᪷r⚪ᑡ_.aoᦪV᪆pKᑖ.26.ூᫀ௃V(1)v/.ABC=a,AD//BC,Z.A+/.ABC=180°.vZ.ADC=/.ABC=a,:.AA+Z,ADC=180°.AB//CD,DAD“BC,ABC஺f(2)ᙠABC஺AD//BC,--EBC=Z-AEB,BEᑖ4BC,•-ABE=Z.AEB9•••AB=AE=273,BH1ADDAḄiH,16⚓ᐳ18⚓

16•AHB=90°,vZ.ABC=30°,AD//BC,:•HAB=cABC=3U0,BH=)B=ᨵ,:.SMBE=\AEFH=ix2V3xV3=3(3)জ£”ᙠCO=/G1BEQCḄiG.¤3-AGLBE,AH1CD,G=Z.BFA=90°-(HAG.NB4F=Z.AHG=90°,AB=AH,•••4G”gZk8M(44S),•.GH=AF9BEᑖ/ABC,AD//BC,•.Z^ABE=EBC,EBC=Z.AEB,•••ABE=Z-AEB,•AB—AE=CD,•••Z.BAG=Z-EAG-zG,AAD=DG,DE=AD-AE=DG-CD=CG,CG=GH-CH=AF-CH,.DE=AF-CHfᓽDE+CH=AFঝ᝞¤4,£”ᙠ஺CḄ=

17AEᑣCE=AD-AE=DG-CD=CG,CG=GH+CH=AF+CH,■■■DE-CH=AF.ூV᪆௃(1)§¨©ªAB஻CD,e©ABC஺f(2)BHJ.ADDAḄiᵫ«¬}¬Ḅឋed3HḄᵫ}¬Ḅ☢¯°pedVf(3)ᑖjk~ᵫᐰh}¬ḄᑨuRឋedV.⚪<ᔠ⚪ὃ´Ḅឋ«¬}¬Ḅឋᐰh}¬ḄᑨuRឋᑭᵨᑖµ¶V·¸⚪⚪Ḅᐵ.18⚓ᐳ18⚓