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A simple cubic

Source: Indian RMO 1999 Problem 4

October 26, 2005

Problem Statement

If p,q,rp,q,r are the roots of the cubic equation x3−3px2+3q2x−r3=0x^3 - 3px^2 + 3q^2 x - r^3 = 0, then show that p=q=rp = q =r.
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