Question 7
A1 (USA) IMO2. Let $a,b,c$ be positive real numbers with product $1$. Prove that
$$\left(a-1+\frac1b\right)\left(b-1+\frac1c\right)\left(c-1+\frac1a\right)\le1.$$
$$\left(a-1+\frac1b\right)\left(b-1+\frac1c\right)\left(c-1+\frac1a\right)\le1.$$