Question 7
If $x_1$, $x_2$ and $x_3$ are the roots of $x^3 - a x^2 + b x - c = 0$, prove that
$$
(x_1 - x_2)^2 + (x_2 - x_3)^2 + (x_3 - x_1)^2 = 2a^2 - 6b.
$$
$$
(x_1 - x_2)^2 + (x_2 - x_3)^2 + (x_3 - x_1)^2 = 2a^2 - 6b.
$$
MathNet 2011 Question 7
Math Olympiad Vault · MathNet 2011