Question

prove that: (x-y)³+(y-z)³+(z-x)³=3(x-y)(y-z)(z-x)

Answer 1

Let (x-y) = a, (y-z) = b and (z-x) = c.

Now, a + b + c = x - y + y - z + z - x = 0.

And, we know that if a +b + c = 0 then,

a^2 + b^2 + c^2 = 3abc

=> (x-y)^2 + (y-z)^2 + (z-x)^2 = 3(x-y)(y-z)(z-x).