Corrective

$a$ ; $m$ ; $n$ are three number such that $m > a - 1 > 0$ and $n > a > 0$ . Is the following inequality true of false? $\large \displaystyle m + n + a \ge 2(\sqrt{m - a + 1} + a\sqrt{n - a})$

Bonus

• If the inequality is correct, prove the inequality is correct.

• If the inequality is incorrect, what minor change could have been made to make the inequality correct?