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x^3 + ax^2 + bx + c , x^3 +α^3 x^2 + β^3 x + γ^3, 3 real roots each, related

Source: Vietnam MO 1979 P2

July 28, 2018
algebraPolynomials

Problem Statement

Find all real numbers a,b,ca, b, c such that x3+ax2+bx+cx^3 + ax^2 + bx + c has three real roots α,β,γ\alpha, \beta,\gamma (not necessarily all distinct) and the equation x3+α3x2+β3x+γ3x^3 + \alpha^3 x^2 + \beta^3 x + \gamma^3 has roots α3,β3,γ3\alpha^3, \beta^3,\gamma^3 .
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