MathDB
x^2-2mx-1=0, x_1^3+x_2^3=8(x_1+x_2)

Source: 2001 Austria Beginners' Competition p2

October 4, 2022
algebraquadratic polynomialQuadratic

Problem Statement

Consider the quadratic equation x2−2mx−1=0x^2-2mx-1=0, where mm is an arbitrary real number. For what values ​​of mm does the equation have two real solutions, such that the sum of their cubes is equal to eight times their sum.
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