Question 38
Let $a$, $b$, $c$ and $d$ be real numbers with $a^2 + b^2 + c^2 + d^2 = 4$. Prove the inequality
$$(a+2)(b+2) \geq cd$$
and give four numbers $a$, $b$, $c$ and $d$ such that equality holds.
$$(a+2)(b+2) \geq cd$$
and give four numbers $a$, $b$, $c$ and $d$ such that equality holds.