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Relation between Roots and Coefficients for Quadratic

If alpha, bet...

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If alpha, beta and gamma are the roots of the equation x^3+4x+1=0, then (alpha+beta)^-1 + (beta+gamma)^-1 + (gamma+alpha)^-1 is

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α, β, γ

x^{3} - 6 x - 4 = 0

, then the equation whose roots are

β γ + \frac{1}{α}, γ α + \frac{1}{β}, α β + \frac{1}{γ}

α, β, γ

are the roots of the equation

x^{3} + 4 x + 1 = 0

(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1} =

α, β, γ

are the roots of

x^{3} + q x + r = 0

\frac{1}{α + β - γ} + \frac{1}{β + γ - α} + \frac{1}{γ + α - β} =

α, β, γ

are the roots of

x^{3} + a x + b = 0

(α + β)^{- 1} + (β + γ)^{- 1} + (γ + α)^{- 1} =

x^{3} + 5 x^{2} - 7 x - 1 = 0

α, β, γ

, then the equation whose roots are

α β, β γ, γ α

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