(ab²-a²b)÷(a-b) 已知（x+y）²-2x-2y+1＝0,求2x²+4xy+2y²

题目

(ab²-a²b)÷(a-b) 已知（x+y）²-2x-2y+1＝0,求2x²+4xy+2y²
已知4x²+y²-4+6y+10=0,求4x-12xy+9y²

答案

(ab²-a²b)÷(a-b)
= ab(b-a) ÷(a-b)
= - ab
(x+y) ² - 2x-2y+1=0
(x+y)²-2(x+y)+1=0
(x+y-1)²=0
x+y-1=0
x+y=1
2x²+4xy+2y²
=2(x+y)²
=2
4x²+y²-4x+6y+10=0
4x²-4x+1+y²+6y+9=0
(2x-1)²+(y+3)²=0
2x-1=0 ,y+3=0
x=1/2,y= -3
4x²-12xy+9y²
= (2x-3y)²
= 100