已知x²-4x+4+（y+x的绝对值）=0,求x²y-x²分之2x+x²÷y²-2y+1分之x²+4x+4

题目

已知x²-4x+4+（y+x的绝对值）=0,求x²y-x²分之2x+x²÷y²-2y+1分之x²+4x+4
另外还有一题：已知x-3y=0,求x²-2xy+y²分之2x+y×（x-y)的值.

答案

x²-4x+4+（y+x的绝对值）=0,则(x-2)²+|y+x|=0
则x-2=0,y+x=0,则x=2,y=-2
x²y-x²分之2x+x²÷y²-2y+1分之x²+4x+4
=x²(y-1)分之x(x+2)÷(y-1)²分之(x+2)²
=x(y-1)分之(x+2)×(x+2)²分之(y-1)²
=x(x+2)分之(y-1)
=2×(2+2)分之(-2-1)
=-8分之3
x-3y=0,则x=3y
x²-2xy+y²分之(2x+y)×（x-y)
=(x-y)²分之(2x+y)×（x-y)
=(x-y)分之(2x+y)
=(3y-y)分之(6y+y)
=2y分之7y
=2分之7