Question

已知x+y=3,xy=2,求代数式x^3+x^2y+xy^2+y^3的值

Answer 1

x+y=3

两边平方

x^2+y^2+2xy=9

x^2+y^2=9-2xy=9-4=5

x^3+x^2y+xy^2+y^3

=(x^3+y^3)+(x^2y+xy^2)

=(x+y)(x^2-xy+y^2)+xy(x+y)

=3*(5-2)+2*3

=15