Question 79
Let $a,b,c$ be positive real numbers with $abc\ge1$. Prove
$$\frac{a^4-1}{ab^3+abc+ac^3}+\frac{b^4-1}{bc^3+abc+ba^3}+\frac{c^4-1}{ca^3+abc+cb^3}\ge0.$$
$$\frac{a^4-1}{ab^3+abc+ac^3}+\frac{b^4-1}{bc^3+abc+ba^3}+\frac{c^4-1}{ca^3+abc+cb^3}\ge0.$$