题目

若x-y=5,xy=14,则x3-x2y+xy2-y3=?

提问时间：2020-10-23

答案

x-y=5,xy=14
x²+y²=(x-y)²+2xy=5²+2×14=53
x³-x²y+xy²-y³
=x³-y³-x²y+xy²
=(x-y)(x²+xy+y²)-xy(x-y)
=(x-y)(x²+xy+y²-xy)
=(x-y)(x²+y²)
=5×53
=265