Prove An Equation - Proof Required Please

[Ritu]

If

(x + y + z) = 0

show that

(x^2 + y^2 + z^2)^2 = 2 ( x^4 + y^4 + z^4)

 

[stapel]

What have you tried? How far did you get? Where are you stuck?

You squared x[sup:21wp16e3]2[/sup:21wp16e3] + y[sup:21wp16e3]2[/sup:21wp16e3] + z[sup:21wp16e3]2[/sup:21wp16e3] and simplified. You squared x + y + z, noting that zero squared is still zero, and created an equivalence between x[sup:21wp16e3]2[/sup:21wp16e3] + y[sup:21wp16e3]2[/sup:21wp16e3] + z[sup:21wp16e3]2[/sup:21wp16e3] and the sum of terms in xy, xz, and yz. You squared this result, and... then what? Or, if you went another way, what were your steps?

Please be complete. Thank you!

Eliz.