Question 115
If $a_1, a_2, \dots, a_n$ are positive real numbers such that
$$
t = a_1 + a_2 + \dots + a_n = a_1^2 + a_2^2 + \dots + a_n^2
$$
and $n \ge 2$, then show that
$$
\sum_{i \neq j} \frac{a_i}{a_j} \geq \frac{(n-1)^2 t}{t-1}.
$$
$$
t = a_1 + a_2 + \dots + a_n = a_1^2 + a_2^2 + \dots + a_n^2
$$
and $n \ge 2$, then show that
$$
\sum_{i \neq j} \frac{a_i}{a_j} \geq \frac{(n-1)^2 t}{t-1}.
$$