已知X+Y=2,求(X²-Y²)²--8(X²+Y²)的值
问题描述：
已知X+Y=2,求(X²-Y²)²--8(X²+Y²)的值
答
已知X+Y=2
(X+Y)²=X²+Y²+2XY=4
X²+Y²=4-2XY
(X²-Y²)²--8(X²+Y²)
=(X²+Y²)²-8(X²+Y²)-4X²Y²
=(X²+Y²)(X²+Y²-8)-4X²Y²
=(4-2XY)(4-2XY-8)-4X²Y²
=-(4-2XY)(4+2XY)-4X²Y²
=-16