已知13x^2-6xy+y^2-4x+1=0,求(xy-x^2)^3的值.

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已知13x^2-6xy+y^2-4x+1=0,求(xy-x^2)^3的值.
已知13x^2-6xy+y^2-4x+1=0,求(xy-x^2)^3的值.

已知13x^2-6xy+y^2-4x+1=0,求(xy-x^2)^3的值.
13x^2-6xy+y^2-4x+1=0
(9x^2-6xy+y^2)+4x^2-4x+1=0
(3x-y)^2+(2x-1)^2=0
加数均非负,和为0.则均为0
所以有：
3x=y
2x-1=0
x=1/2
y=3/2
(xy-x^2)^3
=(3/4-1/4)^3
=1/8

13x^2-6xy+y^2-4x+1=0
（4x^2-4x+1）+(9x^2-6xy+y^2)=0
(2x-1)^2+(3x-y)^2)=0
∴2x-1=0,x=1/2
y=3/2
（xy-x^2)^3=（1/2*3/2-1/2^2)^3=1/8

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