Question 76
Let $a$, $b$, $c$, and $d$ be real numbers such that $a \geq b \geq c \geq d$ and
$$
\begin{aligned}
a+b+c+d & = 13 \\
a^{2}+b^{2}+c^{2}+d^{2} & = 43
\end{aligned}
$$
Show that $ab \geq 3 + cd$.
$$
\begin{aligned}
a+b+c+d & = 13 \\
a^{2}+b^{2}+c^{2}+d^{2} & = 43
\end{aligned}
$$
Show that $ab \geq 3 + cd$.