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If $α, β, γ$ are the cube roots of $p, p < 0,$ then for any x, y and z which does not make denominator zero,
the expression $\frac{x α + y β + z γ}{x β + y γ + z α}$

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ω , 1

ω , ω2

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detailed solution

Correct option is B

x3=p=p133⇒x=p13,p13ω,p13ω2Let α=p13,β=p13ω,γ=p13ω2 xα+yβ+zγxβ+yγ+zα=x+yω+ω2zxω+yω2+z=1ω=ω2If α=p13ω,β=p13,γ=p13ω2 then , xα+yβ+zγxβ+yγ+zα=1ω2=ω.

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If α , β , γare the cube roots of p, p < 0, then for any x, y and z which does not make denominator zero, the expression xα+yβ+zγxβ+yγ+zα

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $α, β, γ$ are the cube roots of $p, p < 0,$ then for any x, y and z which does not make denominator zero,
the expression $\frac{x α + y β + z γ}{x β + y γ + z α}$