Question

已知x+y=5,x方+y方=13，求代数式x立方y+2x方y方+xy立方的值

Answer 1

x+y=5,
x方+y方=13=(x+y)^2-2xy
xy=6
x立方y+2x方y方+xy
=xy(x^2+2xy+y^2)
=xy(x+y)^2
=6*5^2
=150

Answer 2

x²+y²
=（x+y）²-2xy
=25-2xy
=13
则2xy=12
xy=6
x³y+2x²y²+xy³
=xy（x²+2xy+y²）
=xy（x+y）²
=6×5²
=150