#1516 · Algebra · Linear equations

Symmetric combinations of variables with omega (part 3)

If $1$ , $ω$ , $ω^{2}$ are the three cube roots of unity, and $x = a + b$ , $y = aω + b ω^{2}$ , $z = a ω^{2} + bω$ , shew that $x^{3} + y^{3} + z^{3} = 3 (a^{3} + b^{3})$ .

~8 minProof · checked by AICube roots of unityAlgebraic identity

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VIII. Surds and Imaginary Quantities, Examples VIII.b, No. 30 (part 3)

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