已知4x^2 y^2 xy=1,求2x y的最大值-搜答案-智慧作业帮

=-x-(2y-2+3x)+2(x+4)=-x-2y+2-3x+2x+8=-4x-2y+10

X²+Y²+X²Y²-4XY+1=0(X-Y)^2+(XY-1)^2=0所以X-Y=0XY-1=0（X-Y)^2008-(XY)^2008=0^2008-1^2

因为x-y=4xy所以x-2xy-y=2xy2x+3xy-2y=11xyx-2xy-y分之2x+3xy-2y=5.5

根据已知得到x=-2y=-1原式=5xy^2-{2x^2y-[3xy^2-(4xy^2-2x^2y)]}=5xy^2-{2x^2y-[3xy^2-4xy^2+2x^2y]}=5xy^2-{2x^2y-

(-2xy+2x+3y)-(3xy+2y-2x)-(x+4y+xy)=-6xy+3x-3y=-6×(-2)+3×1=15

答：x+y=-1,xy=-2-5（x+y)+(x-y)+x(xy+y)=-5x-5y+x-y+xy(x+1)=-4x-6y+(-2)(x+1)=-4x-6y-2x-2=-6x-6y-2=-6(x+y)

原式=[4(x+y)-2xy]分之[(x+y)+xy]=[4(3xy)-2xy]分之[(3xy)+xy]=10xy分之2xy=5分之1

3/(x-y)=1/xyx-y=3xyy-z=-3xy原式=[(y-x)-2xy]/[2(x-y)+3xy]=[(-3xy)-2xy]/[2(3xy)+3xy]=-5xy/9xy=-5/9

原式=-2x^2-2y^2-3xy-11xy=-2*7-14*(-1)=0

由已知通分Y-X=4XY所以所求=-2(Y-X）+xy/-（Y-X）-2XY=-7XY/-6XY=7/6

∵1/x-1/y=4∴(y-x)/xy=4∴y-x=4xy∴x-y=-4xy(2x+xy-2y)/(x-2xy-y)=[2(x-y)+xy]/[(x-y)-2xy]=(-8xy+xy)/(-4xy-2

3-y=0x+y=0∴x=-3y=3[2(x+y)-3(xy+4)]÷1／xy=[2×0-3(-9+4)]÷(-1/9)=15×（-9）=-135

5x^2-(3xy+4y^2)-(11xy-2y^2)-7x^2=5x^2-3xy-4y^2-11xy+2y^2-7x^2=-2x^2-2y^2-14xy=-2(x^2+y^2)-14*xy=-2*7

1/x-1/y通分=(y-x)/xy=3y-x=3xyx-y=-3xy所以原式=[3(x-y)+4xy]/[(x-y)-2xy]=[3(-3xy)+4xy]/[(-3xy)-2xy]=-5xy/(-5

（-2xy+2x+3y)-(3xy+2y-2x)-(x+4y+xy)=(-2xy-3xy-xy)+(2x+2x-x)+(3y-2y-4y)=-6xy+3x-3y=-6+3*3=3

①xy同非负时,2x-3√xy-2y=(2√x+√y)(√x-2√y)=0∴√x=2√y,x=4y②xy同负时,2x-3√xy-2y=[2√(-x)+√(-y)][√(-x)-2√(-y)]=0∴√(

同除xy原式变形为：（3/y-4+3/x）/(1/x+2+1/y)=5/5=1

0=x^2+y^2+x^2y^2-4xy+1=x^2+y^2-2xy+x^2y^2-2xy+1=(x-y)^2+(xy-1)^2,两个平方数的和等于0,所以,x=y,xy=1,带入得(x-y)^200

(-2xy+2x+3y)-(3xy+2y-2x)-(x+4y+xy)=-2xy+2x+3y-3xy-2y+2x-x-4y-xy=-6xy+3x-3y=-6*(-2)+3*1=15不懂可追问,有帮助请采