Question 3
Let $a,b,c$ be positive real numbers. Prove that
$$\left(1+\frac ab\right)\left(1+\frac bc\right)\left(1+\frac ca\right)\ge2\left(1+\frac{a+b+c}{\sqrt[3]{abc}}\right).$$
$$\left(1+\frac ab\right)\left(1+\frac bc\right)\left(1+\frac ca\right)\ge2\left(1+\frac{a+b+c}{\sqrt[3]{abc}}\right).$$