已知x+y=4,x2+y2=14,求x3y-2x2y2+xy3的值.

问题描述:

已知x+y=4,x2+y2=14,求x3y-2x2y2+xy3的值.

∵x+y=4,
∴(x+y)2=16,
∴x2+y2+2xy=16,
而x2+y2=14,
∴xy=1,
∴x3y-2x2y2+xy3
=xy(x2-2xy+y2
=14-2
=12.