若(x+y-5)^2+lx-y+3l=0

题目

若(x+y-5)^2+lx-y+3l=0
x^2-y^2=?

答案

因为 (x+y-5)^2 >=0, lx-y+3l >=0, (x+y-5)^2+lx-y+3l=0
所以 (x+y-5)^2 =0, lx-y+3l =0
所以 x+y = 5, x-y = -3
所以 x^2-y^2 = (x+y)*(x-y) = -15