已知x+y=10,xy=24,求x3+y3-x2y-xy2的值
问题描述:
已知x+y=10,xy=24,求x3+y3-x2y-xy2的值
答
x3+y3-x2y-xy2
=(x+y)(x2-xy+y2)-xy(x+y)
=(x+y)(x2-2xy+y2)
=(x+y)(x2+2xy+y2-4xy)
=(x+y)[(x+y)2-4xy]
=10×(100-96)
=40