Question 44
Let $a$, $b$ be two distinct real numbers and let $c$ be a positive real number such that
$$
a^4 - 2019a = b^4 - 2019b = c.
$$
Prove that $-\sqrt{c} \lt ab \lt 0$.
$$
a^4 - 2019a = b^4 - 2019b = c.
$$
Prove that $-\sqrt{c} \lt ab \lt 0$.
MathNet 2019-part-03 — 184 problems (EN–VI) Question 44
Math Olympiad Vault · MathNet 2019-part-03 — 184 problems (EN–VI)