Question

If x + y + z = 1, 1x+1y+1z=11x+1y+1z=1 and xyz = 1, then x3 + y3 + z3 is equal to

Answer 1

x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx)

x³+y³+z³=(x+y+z)(x²+y²+z²-xy-yz-zx)+3xyz

x³+y³+z³=1x(x+y+z)²-1+3x-1
=1-1-3
=-3