If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
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Solution
We know that,
x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – xz)
Now put (x + y + z) = 0,
x3 + y3 + z3 - 3xyz = (0)(x2 + y2 + z2 – xy – yz – xz)
⇒ x3 + y3 + z3 – 3xyz = 0
⇒ x3 + y3 + z3 = 3xyz
Concept: Algebraic Identities
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