MathDB
polynomial

Source: Austria 1983

July 7, 2009
algebrapolynomialalgebra unsolved

Problem Statement

Let x1,x2,x3 x_1,x_2,x_3 be the roots of: x^3\minus{}6x^2\plus{}ax\plus{}a\equal{}0. Find all real numbers a a for which (x_1\minus{}1)^3\plus{}(x_2\minus{}1)^3\plus{}(x_3\minus{}1)^3\equal{}0. Also, for each such a a, determine the corresponding values of x1,x2, x_1,x_2, and x3 x_3.
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