If satisfy If biquadratic equation has the roots

MATHEMATICS · Single correct · AoPS · Mathematics · More Inequalities · More Inequalities

Problem

If α,β,γ,δ∈R\alpha, \beta, \gamma, \delta \in R satisfy (α+1)2+(β+1)2+(γ+1)2+(δ+1)2α+β+γ+δ=4\frac{(\alpha+1)^2 + (\beta+1)^2 + (\gamma+1)^2 + (\delta+1)^2}{\alpha + \beta + \gamma + \delta} = 4 If biquadratic equation a0x4+a1x3+a2x2+a3x+a4=0a_0x^4 + a_1x^3 + a_2x^2 + a_3x + a_4 = 0 has the roots (α+1β−1),(β+1γ−1),(γ+1δ−1),(δ+1α−1)\left(\alpha + \frac{1}{\beta} - 1\right), \left(\beta + \frac{1}{\gamma} - 1\right), \left(\gamma + \frac{1}{\delta} - 1\right), \left(\delta + \frac{1}{\alpha} - 1\right). Then the value of a2/a0a_2/a_0 is: (a) 4 (b) -4 (c) 6 (d) none of these

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