2021-2022学年高一上学期数学人教A版必修第一册【高一数学】基本不等式同步练习卷

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2.2
ᔁஹᓫ⌱⚪41.x>l,ᑣy=2x+—ḄᨬX-1A.4&B.472+2C.4a+1D.2+22.x>0,y>0,x+2y-\,ᑣ+ḄᨬxyA.6B.5C.3+2D.4723.ab>0—I—>2ḄabA.ᐙᑖ!⌕ᩩ$B.!⌕ᐙᑖᩩ$C.ᐙ⌕ᩩ$D.%ᐙᑖ&!⌕ᩩ$4."(beR,)!H0,ᑣ*ᑡ,-ឤᡂ0ḄA.ab>2^bB.+a+bுJ/+2c.D.a2+h2>2ab45.a>0,ᑣQ-IHḄᨬaA.-1B.3C.4D.5856.2>0,y>0,)xy=10,ᑣ3ᓝḄᨬyA.2B.3C.4D.67.a,b567ᦪ(2a+b=l,ᑣ9Ḅᨬᜧ2111A.-B.-C.D.:98428.*ᑡ;ᦪ<ᨬ4Ḅ1?+2x+5A.y=4x+—B.=x>0>(V-,XX+131D.y=^lx2+54c.=>(y=2x1+22x-3+5@ஹA⌱⚪9.B஻>0,b>0,ᑣ*ᑡឤᡂ0ḄA.a+-^->7B.a2+^—>]C.D^22D.fa+-Y&+->|>4a-3a2+l4abIaAb1910.X,y6ᦪ()E=1,(஻=x+y,n=-+~,*ᑡ⌱⚗<6HḄᨵA.JḄᨬ2B.஻Ḅᨬ6C.Ḅᨬ16D,஻?+஻Ḅᨬ5

111.6ᦪx,yQRx+y=2,ᑣ*ᑡ⌱⚗6HḄ()A.'+(Ḅᨬ2B.YḄᨬᜧ2xyC.f+᮱Ḅᨬ4D.x(y+l)Ḅᨬᜧ`12.ab*☢defg(ᐸ<6HḄ()A.ia,bc(O,w),ᑣabB.ab=4,opJa+Z?24c.ia>0,b>0,ᑣ(4+2»(v+3)ᨬ4xߟz7c|2bh+nb+mD.a>b>0,m>n>0,ᑣv----<-----aa+na+niஹ⚪413.y=3x+—(x>0),yᨬ>xḄ.x14.67ᦪ஻(஻QRa+2Z?=4,oIJ"Ḅᨬᜧ.15.67ᦪa,b=6,ᑣ(a+l)S+9)Ḅᨬ.216.21++—>()ᑗX£(l,”)ឤᡂ0(ᑣ7ᦪ஻?Ḅ_________.X-1dஹ⚪17.(1)஺3,>=^+Ḅᨬ.2X—318.(1)i7ᦪx>l,x+_1Ḅᨬ(>xḄx-1(2)ix<0,Ḅᨬᜧ(>xḄ.X19.(1)x>0,y>o,)2x+3y=l,ᑘḄᨬᜧফx>0,y=+x+lḄᨬ2xᔁ22⚓(ᐳ3⚓

220.(1)¡஻ஹ)a>0,6>0)4a+b=l,!Ḅᨬᜧ;(2)£ஹycR)x>0,y>05.9x+y=xyᐗ+yḄᨬ.f41621.(1)x>2,x+—^Ḅᨬ(2)ix>0>(1--Ḅᨬᜧ.x-2x22.(1)ix>0,y>0,x+3y=l,¥¦Ḅᨬ.(2)0xḄ;

32.2
ᔁᫀ1.Bூ
௃«X>1,ᡠ1>0,ᡠy=2xH----=2(x—1)H-----F222^2(x—1)----+2=4A/2+2,X1X"""1yX14=)°=2஺-1)=-ᓽ=/+1>³(x-\4ᡠy=2x+—Ḅᨬ40+2(x-1ᦑ⌱vB2.Cூ
௃«x>0,y>0,x+2y=\,ᑣ_L+L(x+2y)d+L)=3+·+223+2&x±=3+2(xyxyxy\xy=)°==¹>(ᓽº=2-—2>,³ᡂ0(Xy66ᡠ'Ḅᨬ3+2VLxyᦑ⌱vC.3.Bூ
௃¼^,v=஺=b=l>(QR4஻=1>0,½—I——2,—I—>2ᡂ0(ᦑ஽6>0—F—>2ahahabḄᐙᑖᩩ$="<0>2+f2ᡂ0(=¿=0>2+/ÀÁÂ(ᓽ2+(>2ᡂ0,ababababᦑ">0>2Ḅ!⌕ᩩ$abæ(">0Ä+:>2Ḅ!⌕ᐙᑖᩩ$.ab¼@v=!>0>(->0,y>0,᜛+422ஹÇ2=2,=)°=>³(abab\abᡠ!>02+f>2Ḅᐙᑖᩩ$abᫀ24⚓(ᐳ9⚓

4i2+3>2,ᑣ2+@=ɱC>2,ᡠ!>0,ᦑ">0Ê+Ë>2Ḅ!⌕ᩩ$cibabababæ(H>0Ä+f>2Ḅ!⌕ᐙᑖᩩ$.abᦑ⌱vB.4.BூÍ௃A,a=-l,b=-2,ᑣa+622Ïᡂ0,ᦑ⌱⚗A┯ÑB,«:ÒÓ³(ᡠ£+vᵨ+᪍>2Öᵨ=2,=)°=஺=£>³,ᦑ⌱⚗B6HCva=T,b=-2,ᑣᡂ0(ᦑ⌱⚗C6HDv஺=1,h=\,ᑣ/+82=2Ø7,ᦑ/+/>2"ᡂ0(ᦑ⌱⚗D6Hᦑ⌱vB.5.BூÍ௃ᵫ⚪Á(஻>0,᪷Ûᙳ44I~4Q-1+—=஺+——1>2,ax1=4-1=3aaVa4=)°=஺=(ᓽ஺=2>³ᡂ0aᦑ⌱vB6.CூÍ௃«x>0,)>0,)ß=10,ᡠà22H=2á4,85=)°==ᓽx=4,y=g>³(xy2Q5ᡠ+Ḅᨬ4,xyᦑ⌱vC7.BூÍ௃«“(ᑖ567ᦪ(2a+b=l,ᫀ25⚓(ᐳ9⚓

5@ᔆåஹ1,2ab,1/2a+b\1ᡠ!=——<------22}8=)°=æᔣᓽ஺=᝞=;>(éᨬᜧᶌᦑ⌱vB8.BூÍ௃A,y=4x+—,᝞ëxvO>(y<0,ᦑAìᔠ⚪Á;x(x+l7+44B,«(J+2-+5+ஹ4,=(X+1)H------22X+1x+1v7x+\X+14=)°=x+l
=tî(ᓽx=l>³(ᦑB6H;C,«ï2xT+ð+2<-2+2=0,=)°=.2ñ-3=2(ᓽò=1>³(ᡠᐸᨬ0,ᦑC┯Ñ;D,y=ylx2+5+-^>2Hx2+5x^L==4,=)°=Jx?+5=7)ᓽ>r«+5VyJx2+5(r+5À(ó⊤õᨬ4ᑮ(ᦑD┯Ñ.ᦑ⌱vB.9.BCDூÍ௃Av«஺>0,ᡠa—3Ḅì³÷(44øᯠ(=a=2>(a+—ᡂ0(a-32-3ᓽ⌱⚗A┯ÑBv«a>0,ᡠᡠúH;=+14-------1>2./fl2+1
—5-------1=1ᡂv'7v,a2+la2+\Va+1«ᡠY+IH-@(ᓽûᑮ³(4~+1ᓽ⌱⚗B6HCv«a>0,/?>0,ᡠa+Z?22\[ab>0,ᫀ26⚓(ᐳ9⚓

6ᡠr௄22(=)°=஺=6>0>³),7abᓽ⌱⚗C6HDv«஺>0,b>(),(=)°=()ý=:(ᓽ“=0=1>³),abᓽ⌱⚗D6H.ᦑ⌱vBCD.10.ABCூ
௃ᵫ⚪Á(7ᦪò,)'6ᦪ()E=1,þ©y=ÿX
=x+yN2=2,x=y=lᡂᡠᵨḄᨬ2,ᡠAᵫ2,=9x,ᓽx=:,y=3ᡂ,xyxvxx3ᡠ஻Ḅᨬ6,ᡠBᵫn7n=(x+y)(—+—)=10+—+—>10+2/—8—=16,xyxyyxy^ᓽx=3,y=&ᡂxy3ᓽ஻!Ḅᨬ16,ᡠC;ᵫ#=1,
y=,X[9]]2I2$Um+஻=x+—+y+—=*+—4----F9X=10X+—>2./10XX—=4,xyxxXVxx=*,y=%ᡂᡠḄᨬ4&ᡠD%.ᦑ⌱*ABC.11.BCூ
௃+ᦪ-./0*+y=2,111ᵫL_+_=3x1Xy2+y(x+4.5ᫀ77⚓ᐳ9⚓

7:=2ᓽx=y=lᡂᡠAxyᵫx+yN2
242,ᓽ#41,x=y=1ᡂᡠB┯<ᵫV+y2=(x+y)2—2?=4-2@±4-2=2,x=y=lᡂᡠC┯<ᵫᦪMY/0x+y=2,
x+(y+l)=3,ᑣx(y+l)4(BCD=E+1319ᓽx=y=ᡂᓽx(y+DḄᨬᜧG*ᡠD.ᦑ⌱*BC.12.ADூIJ௃A.+஺M€(0,+<»),ᑣ2+0=2ᓈ=2,ᓃ?,ᓽa=bᡂᦑab\ahabB.^a=-2,b=-2,ᑣa+6=~4,ᦑ┯<C.+a>0,b>0,ᑣ(a+2Pj2+]=3+Q+⁐23+2*/ᦋ@=3+2U\ab)ab\ab—=7,ᓽa=Vᡂᦑ┯<abbb+n(b-a)nb+mb+n(b-a\(n-m\D.+a>6>0,m>n>0,ᑣ-------\<0,----------------------------=)~?ߟ(>0,ᦑaa+na\a+n)a+ma+n[a+m)[a+n).ᦑ⌱*AD13.,3ூIJ௃+x>0,ᡠᵫᙳ%Y
y=3x+->2.£r3=4^,X\X3x=3ᓽx=2Zy=3x+±[ᨬ4\.x3xᦑ5ᫀ*,.314.2ூIJ௃5ᫀ78⚓ᐳ9⚓

8ᵫ]ᦪm8/0a+2Z?=4,—TZH,1…-1(a+2b|="2.
"=—42Z?K---------222஺=2A=2"[ᨬᜧ2.ᦑ5ᫀ*215.16ூIJ௃19+]ᦪ஺ᓃ/0a+=6,abᡠ6=,+222*bᓽ21,cᓽd21,ahVah21Q1•g*ᓽ஺=*h=3[.ab319+a+1=6,ᡠ/b+9a=6ab,abᡠ(a+l)S+9)=9a+b+"+9=7"+927+9=16.ᦑ(஻+1)஺+9)ḄᨬG16.ᦑ5ᫀ*1616.m>—6ூIJ௃22J*%Y2x+"?+——>0ᓄ*23-1)+——->-//7-2,x-1X-1Qx>l,/.2(x-l)-t-^—..2x2(x-l)»—^—=4,x=2[.x-1Vx-12:%Y2x+m+——>0kaᑗX€(1,+»)ឤᡂX-1/M—2<4,J/??>-6,ᦑ5ᫀ*m>—6.17.(1)ᨬᜧJ(2)ᨬ7.OூIJ௃(1)+ᡠ1a2q>0,ᡠy=x(l_2x)=g.(2ᐗ).(I_2x)ீg2t2u=05ᫀ79⚓ᐳ9⚓

9213ᓽx4ᡂ,ᡠy=x(l-2x)Ḅᨬᜧ{O4(2)+x>3,ᡠ~—3>(),—>0,x-344ᡠC+ᡝ!+1+3.2•(x—3)+3=7.=ᓽ=5ᡂ,x>34ᡠE=g+”Ḅᨬ7.1418.(l)x+—ḄᨬG3,x=2ফx+aḄᨬᜧG-4,~=-2.a1XூIJ௃(1)+]ᦪX>1,ᑣXH----=(X—1)H------F122.(X—1)----F1=3,X—1=~x-1x-\Vx-1x-\[“=”ᵫ%>1-1g---7J*~=2,x-1ᡠx+—1ḄᨬG3,x=2x-\4T4I4~4(2)+xvO,ᑣ+aga(au+a<-2J(-x)•a=-4,aY=a[”xL-xjV-x-X4ᵫx<0—X=—J*x=—2,-xᡠx+ḄᨬᜧG4,q=a2.X1319.(1)—(2)242ூIJ௃1…<1(21+3ு111(1)=-x———,64242x=3y=Jᡂ.5ᫀ710⚓ᐳ9⚓

10x=Lx=1ᡂ.20.(1)—(2)16.16ூIJ௃(1)+beRS.a>0,b>Q,ᵫ%Y
1=+275^=4,ᡠab<^-,஻=4஺ᡂ+᝛Ḅᨬᜧg16y+9x19(2)+xஹyeRx>0,y>09x+y=_xy,$1]^----=a+-=1,xyxyy=3xᡂᦑ+yḄᨬ16.41621.(1)xH---■Ḅᨬ6(2)1—xḄᨬᜧ-7.x-2xூIJ௃(1)ᵫx>2,x—2>0,ᡠx+^-=x-2+^-+222,(x-2)(^-]+2=6,%-2X—2y2J44~-2=Tᓽx=4ᡂᡠx+§Ḅᨬ6x-2x-2(2)ᵫx>0,Wl-A*--=l-fx+—=-7,x=3,ᓽx=4x\xJVxxᡂᡠl-x--Ḅᨬᜧ-7.x4222.(1)4(2)ᨬᜧx=§ூIJ௃J*(1)+x>0,y>0,x+3y=l,ᡠ111±(x+3y)=2+?+®2+2¯4=4,§°ᓽ—I---=+x3yx3yq=2y=1[,265ᫀ711⚓ᐳ9⚓

11ᡠḄᨬ4x3yP-]2c(2)+0