MathDB

2

Part of 2001 Austria Beginners' Competition

Problems(1)

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

Source: 2001 Austria Beginners' Competition p2

10/4/2022
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.
algebraquadratic polynomialQuadratic