3x y=1,求x^2 y^2的最小值

1/x+1/y=5（y+x）/xy=5x+y=5xy2x-3xy+2y/x+xy+y=2（x+y）-3xy/(x+y)+xy=10xy-3xy/5xy+xy=7xy/6xy=7/6如果本题有什么不明白

1/x+1/y=3∴x+y=3xy3x-2xy+3y/x+xy+y=[3(x+y)-2xy]/[(x+y)+xy]=(9xy-2xy)/(3xy+xy)=7/4

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

因为1/x+1/y=3所以x+y=3xy所以x+xy+y/2x-3xy+2y=（3xy+xy)/(6xy-3xy)=4xy/3xy=4/3

1/x+1/y=5(x+y)/x*y=5x+y=5*x*yx+2xy+y=x+y+2xy=5xy+2xy=7xy2x-3xy+2y=10xy-3xy=7xy(x+2xy+y)/(2x-3xy+2y)=

1上下同除以xy,原式=(2/y-2/x-3)/(1/y-1/x-2)=6/52原式两边平方可得x平方+x平方分之一=11(2)所求式子平方,即原式的平方=x平方+x平方分之一+2=13,所以原式=正

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

1/x-1/y=3(y-x)/xy=3y-x=3xyx-y=-3xy(2X+3XY-2Y)/(X-2XY-Y)=[2(x-y)+3xy]/[(x-y)-2xy]=(-6xy+3xy)/(-3xy-2x

1/x+1/y=(x+y)/xy=8x+y=8xy2x-3xy+2y/x+2xy+y=[2(x+y)-3xy]/[(x+y)+2xy]=(16xy-3xy)/(8xy+2xy)=13xy/10xy=1

原式=3x-3y-6xy=3-12=-9

（1/X）-（1/Y）=3(y-x)/xy=3y-x=3xyx-y=-3xy(2X+3XY-2Y)/(X-2XY-Y)=[2(x-y)+3xy]/[(x-y)-2xy]=(-6xy+3xy)/(-3x

(-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*

(x+xy+y)/(2x-3xy+2y)的上下各项均除以xy得(1/y+1+1/x)/(2/y-3+2/x)=(1+3)/(6-3)=4/3☆⌒_⌒☆希望可以帮到you~

1/x-1/y=2等式两边同时乘以xyy-x=2xyx-y=-2xy=[2(x-y)+3xy]/[(x-y)-xy]=(-4xy+3xy)/(-2xy-xy)=(-xy)/(-3xy)=1/3

分子,分母同时除xy(3/y-5-3/x)/(-1/y+3+1/x)=(6-5)/(3-2)=1

设x=2cosθ,y=sinθ,则x+y=2cosθ+sinθ=√5sin(θ+φ),所以最大值是√5,最小值是-√5xy=2sinθcosθ=sin2θ,所以最大值是1,最小值是-1第三题,（y-2

用数形结合的方法来做.(x-2)²+(y-2)²=1可以看做是以(2,2)为圆心,1为半径的一个圆.y/x可以看做是这个圆上一点到原点连线的斜率.要求y/x的最值,就是求斜率的最值

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

因为1/x+1/y=5y/xy+x/xy=5(x+y)/xy=5所以x+y=5xy所以(2x-3xy+2y)/(x+2xy+y)=[2(x+y)-3xy]/[(x+y)+2xy]=(2×5xy-3xy

(-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