Question

已知x+y+z=1,x2+y2+z2=2,x3+y3+z3=3,求xy(x+y)+yz(y+z)+zx(z+x)的值

Answer 1

∵(x+y+z)(x²+y²+z²)=x³+y³+z³+x²(y+z)+y²(x+z)+z²(x+y)

∴1*2=3+xy（x+y）+yz（y+z）+zx（z+x）

∴xy（x+y）+yz（y+z）+zx（z+x）=2-3=-1