<s>[INST] How to solve system of equations involving square roots How to solve the following system of equations? I've tried some basic techniques like adding/substracting and squaring but with no effect.
$$
\left\{ 
\begin{array}{c}
\sqrt{1 + x_1} + \sqrt{1 + x_2} + \sqrt{1 + x_3} + \sqrt{1 + x_4} = 2\sqrt{5} \\ 
\sqrt{1 - x_1} + \sqrt{1 - x_2} + \sqrt{1 - x_3} + \sqrt{1 - x_4} = 2\sqrt{3}
\end{array}
\right. 
$$
 [/INST] HINT:-
Since the roots have to be positive, we see that each radical must reduce to the form $a\sqrt5$ for the first equation , and $b\sqrt3$ for the second equation.
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