Sum of Squares

Level pending

If $4cos \frac{\pi}{5} + cot \frac{\pi}{24}$ = $\sqrt{n_1} + \sqrt{n_2} + \sqrt{n_3} + \sqrt{n_4} + \sqrt{n_5} + \sqrt{n_6}$ ,

find $\sum_{i=1}^6 n^{2}_i$ .

$Note$ : $All$ $n_i$ $'s$ $are$ $natural$ $numbers.$

1 solution

Guilherme Dela Corte
Dec 26, 2013

WARNING: This problem is bad stated:

We have, amid the $n_i \;$ s, a sum of two integers ( $1 + 2$ ).

If we consider them separate ( $\sqrt{1} + \sqrt{4}$ ), the answer is 91.

If we consider them together ( $\sqrt{9}$ ) , the answer becomes 167.