Question 73
a. The positive real numbers $x,y,z$ have sum $1$. Prove that
$$
\sqrt{7x+3} + \sqrt{7y+3} + \sqrt{7z+3} \leq 7
$$
Can the number $7$ on the right-hand side be replaced by a smaller number?
$$
\sqrt{7x+3} + \sqrt{7y+3} + \sqrt{7z+3} \leq 7
$$
Can the number $7$ on the right-hand side be replaced by a smaller number?