Question 59
Prove that
$$
\sqrt{\frac{1}{3x+1}} + \sqrt{\frac{x}{x+3}} \ge 1
$$
holds for all $x \gt 0$. For which values of $x$ is there an equality?
$$
\sqrt{\frac{1}{3x+1}} + \sqrt{\frac{x}{x+3}} \ge 1
$$
holds for all $x \gt 0$. For which values of $x$ is there an equality?