Question 128
Given real non-zero numbers $a$, $b$, $c$ ($b \gt 0$) so that two distinct roots of the equation $ax^2 + bx + c = 0$ are also the roots of the equation $x^3 + bx^2 + ax + c = 0$.
Prove that a) $abc \gt 16$; b) $abc \ge \frac{3125}{108}$. (V. Karamzin)
Prove that a) $abc \gt 16$; b) $abc \ge \frac{3125}{108}$. (V. Karamzin)