Consider the equation whose roots are, y, z:
(t - x)(t - y)(t - z) = 0
This gives t3 - 3t - λ = 0 where λ = xyz. since x,y,z are root of this equation, we have
x3 - 3x - λ = 0, y3 - 3y - = 0, z3 - 3z - λ = 0
Multiplying the first by y,the second by z and the third by x, we obtain