MathNet 2022-part-02 — 197 problems (EN–VI) Question 147

Suppose $a$, $b$ and $c$ are nonzero real numbers satisfying $abc = 2$. Prove that among the three numbers $2a - \frac{1}{b}$, $2b - \frac{1}{c}$ and $2c - \frac{1}{a}$, at most two of them are greater than $2$.