If \alpha,\beta,\gamma are the zeros of x^3+4x+1, then calcu;ate the

Kason Chang

Kason Chang

Answered question

2022-04-20

If α,β,γ are the zeros of x3+4x+1, then calcu;ate the value of:
(α+β)1+(β+γ)1+(γ+α)1

Answer & Explanation

Pedro Taylor

Pedro Taylor

Beginner2022-04-21Added 19 answers

Note that (α+β)1+(β+γ)1+(γ+α)1=(2α+2β+2γ)3=2(α+β+γ)3. We know from Vieta's formulae that:
α+β+γ=01=0
Therefore, (α+β)1+(β+γ)1+(γ+α)1=2(0)3=3

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