Question

URGENT. I need more questions like the one given below, for practise.

if a = b^2x , b = c^2y , c = a^2z , prove that xyz = 1/8.

Answer 1

1) if a+ b+c= 0 , prove that a^3+ b^3+ c^3 - 3abc = 0
2) if a+ b+ c = 0, prove that
a (b^2+c^2)+b (c^2+a^2)+c (a^2+b^2) =0
3) if a^2+b^2 = c^2+d^2 = 1
then prove that (ac- bd)^2+ (ad+bc)^2 = 0