已知x+y=3,x²+y²-xy=4,求x⁴+y⁴+x³y+xy³的值

问题描述:

已知x+y=3,x²+y²-xy=4,求x⁴+y⁴+x³y+xy³的值

x⁴+y⁴+x³y+xy³
=(x⁴+x³y)+(xy³+y⁴)
=x³(x+y)+y³(x+y)
=(x+y)(x³+y³)
=(x+y)(x+y)(x²+y²-xy)
=(x+y)²(x²+y²-xy)
=3²×4
=36