已知x+y=3,x-y=2,则2x^3y-2xy^3=
问题描述:
已知x+y=3,x-y=2,则2x^3y-2xy^3=
答
x+y=3
∴x²+2xy+y²=9 (3)
x-y=2
x²-2xy+y²=4 (4)
(3)-(4)得
4xy=5
∴xy=5/4
2x^3y-2xy^3=2xy(x²-y²)
=2xy(x+y)(x-y)
=2×5/4×3×2
=15