Question

已知x+y=3,x的平方+y的平方-xy=4,则x的4次方+y的4次方+x的3次方y+xy的3次方的值为?

Answer 1

x+y=3

x²+y²-xy=4

x^4+y^4+x^3y+xy^3

=x^4+x^3y+y^4+xy^3

=x^3(x+y)+y^3(x+y)

=3(x^3+y^3)

=3(x+y)(x²+y²-xy)

=36