Question

已知X2+4y2-4x+4y+5=0 求x-y的值 已知xy=4满足x2y-xy2-x+y=56,求x2+y2的值

Answer 1

X2+4y2-4x+4y+5=(x-2)^2(2y+1)^=0
所以x=2
y=-1/2
所以x-y=5/2

xy=4 所以 x2y-xy2-x+y=4x-4y-x+y=3(x-y)=56
所以 x-y=56/3
x^2+y^2=(x-y)^2+2xy=356

Answer 2

x²+4y²-4x+4y+5=0
(x-2)²+(2y+1)²=0
x-2=0 x=2
2y+1=0 y=-1/2
x-y=2+1/2=5/2
x²y-xy²-x+y=56
xy(x-y)-(x-y)=56
(x-y)(xy-1)=56
(x-y)(4-1)=56
3(x-y)=56
x-y=56/3
x²+y²=(x-y)²+2xy=(56/3)²+8=3208/9

Answer 3

x^2+4y^2-4x+4y+5=0
(x^2-4x+4)+(4y^2+4y+1)=0
(x-2)^2+(2y+1)^2=0
x=2 y=-1/2
x-y=2-(-1/2)=5/2
x^2y-xy^2-x+y=56
xy(x-y)-(x-y)=56（1）
把xy=4代入（1）
4（x-y)-(x-y)=56
x-y=56/3
(x-y)^2=(56/3)^2
x^2+y^2-2xy=(56/3)^2
x^2+y^2=3208/9

Answer 4

1.
x^2-4x+4+4y^2+4y+1=0
(x-2)^2+(2y+1)^2=0
x=2,y=-0.5
x-y=2.5
2.
xy(x-y)-(x-y)=56
(xy-1)(x-y)=56
(x-y)=56/3
x^2+y^2=(x-y)^2+2xy=3208/9