已知x+y=5,xy=4,求:(1)(x+y)2;(2)x2+y2;(3)x-y的值.

问题描述:

已知x+y=5,xy=4,求:(1)(x+y)2;(2)x2+y2;(3)x-y的值.

(1)(x+y)2=52=25;
(2)x2+y2=(x+y)2-2xy=25-2×4=17;
(3)(x-y)2=x2+y2-2xy=17-2×4=9,
则x-y=±

(x−y)2
=±3.