4x^2 y^2 xy=1,求2x y的最小值-搜答案-拍题作业网

=-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

(-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

原式=3x-3y-6xy=3-12=-9

11/4

（4xy+12y)+[7x-(3xy+4y-x)]=4xy+12y+7x-3xy-4y+x=xy+8x+8y=xy+8(x+y)=(-2)+8*3=-2+24=22

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

(-2xy+2x+3y)-(3xy+2y-2x)-(x+4y+xy)=-2xy+2x+3y-3xy-2y+2x-x-4y-xy=-6xy+3x-3y=-6xy+3*(x-y)当时,原式=-6*1+3*

即(x-2y)²=0x-2y=0所以x=2y所以原式=(2x²+2xy-xy-y²)/(4x²-4xy+y²)=(2x²+xy-y²

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

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

得y-x=3xyx-y=-3xy原式=-15xy+2xy/-3xy-4xy=-13/-7=13/7

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