已知(x+y)2=10,(x-y)2=6,求2xy与x2+y2的值.

问题描述:

已知(x+y)2=10,(x-y)2=6,求2xy与x2+y2的值.

∵(x+y)2=10,(x-y)2=6,
∴①x2+2xy+y2=10,
②x2-2xy+y2=6,
①-②得:4xy=4,
∴2xy=2;
①+②得:2x2+2y2=16,
∴x2+y2=8.