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06/07/2021 12:05 pm
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If x + y + z = 0, show that x3+ y3 + z3 = 3xyz.
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06/07/2021 12:07 pm
We know that,
x3+y3+z3-3xyz = (x +y+z)(x2+y2+z2–xy–yz–xz)
Now, according to the question, let (x+y+z) = 0,
then, x3+y3+z3 -3xyz = (0)(x2+y2+z2–xy–yz–xz)
⇒ x3+y3+z3–3xyz = 0
⇒ x3+y3+z3 = 3xyz
Hence Proved