Question 77
Let $a_{1}, a_{2}, \ldots, a_{2005}, b_{1}, b_{2}, \ldots, b_{2005}$ be real numbers such that the inequality
$$
\left(a_{i} x-b_{i}\right)^{2} \geq \sum_{j=1, j \neq i}^{2005}\left(a_{j} x-b_{j}\right)
$$
holds true for every real number $x$ and all $i=1,2, \ldots, 2005$. Find the maximum possible number of the positive numbers amongst $a_{i}$ and $b_{i}, i=1,2, \ldots, 2005$.
$$
\left(a_{i} x-b_{i}\right)^{2} \geq \sum_{j=1, j \neq i}^{2005}\left(a_{j} x-b_{j}\right)
$$
holds true for every real number $x$ and all $i=1,2, \ldots, 2005$. Find the maximum possible number of the positive numbers amongst $a_{i}$ and $b_{i}, i=1,2, \ldots, 2005$.