已知x+y=7,xy=2,求下列各式的值: (1)2x2+2y2的值; (2)(x-y)2的值.
问题描述:
已知x+y=7,xy=2,求下列各式的值:
(1)2x2+2y2的值;
(2)(x-y)2的值.
答
(1)∵x+y=7,
∴x2+2xy+y2=49,
∵xy=2,
∴x2+2×2+y2=49,
解得x2+y2=45,
∴2x2+2y2的值是90;
(2)∵x2+y2=45,xy=2,
∴(x-y)2=x2-2xy+y2,
=45-2×2,
=41.
故答案为:90,41.