Mathematics

Mathematics

Problem

If α,β,γ\alpha, \beta, \gamma are the real roots of the equation x3−3px2+3qx−1=0x^3 - 3px^2 + 3qx - 1 = 0 , then find the centroid of the triangle whose vertices are (α,1α),(β,1β)\left(\alpha, \frac{1}{\alpha}\right), \left(\beta, \frac{1}{\beta}\right) and (γ,1γ)\left(\gamma, \frac{1}{\gamma}\right) .

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