已知:x+y=6,xy=4.(1)求x2+y2的值;(2)求(x-y)2的值;(3)求x4+y4的值.
问题描述:
已知:x+y=6,xy=4.(1)求x2+y2的值;(2)求(x-y)2的值;(3)求x4+y4的值.
答
∵x+y=6,xy=4,
∴(1)x2+y2=(x+y)2-2xy,
=62-2×4,
=28;
(2)(x-y)2=x2+y2-2xy,
=28-2×4,
=20;
(3)x4+y4=(x2+y2)2-2x2y2,
=(x2+y2)2-2(xy)2,
=202-2×42,
=368.