Question 38
Let $a, b, c, d$ be real numbers such that
$$
\begin{aligned}
a+b+c+d & = -2 \\
ab + ac + ad + bc + bd + cd & = 0
\end{aligned}
$$
Prove that at least one of the numbers $a, b, c, d$ is not greater than $-1$.
$$
\begin{aligned}
a+b+c+d & = -2 \\
ab + ac + ad + bc + bd + cd & = 0
\end{aligned}
$$
Prove that at least one of the numbers $a, b, c, d$ is not greater than $-1$.