问题
解答题
已知:xy=4,x2+y2=10,求代数式2x2-2y2的值.
答案
∵xy=4,x2+y2=10,
∴x2+y2+2xy=(x+y)2=10+8=18,x2+y2-2xy=(x-y)2=10-8=2,
∴(x-y)2•(x+y)2=[(x+y)(x-y)]2=18×2=36,
∴(x+y)(x-y)=±6
∵2x2-2y2=2(x+y)(x-y),
∴2x2-2y2=2×6=12或2×(-6)=-12.