已知(x+y)2=18,(x-y)2=6,求x2+y2及xy的值.
问题描述:
已知(x+y)2=18,(x-y)2=6,求x2+y2及xy的值.
答
∵(x+y)2=18,(x-y)2=6,
∴x2+y2+2xy=18,x2+y2-2xy=6,
两式相加得,2(x2+y2)=24,∴x2+y2=12;
两式相减得,4xy=12,∴xy=3.