Basic Inequality - 2

Algebra Level 5

\[\begin{cases} a+3b+4c=25 \\ a^2+b^2+c^2=25 \\ \end{cases} \]

Given that \(a,b\) and \(c\) are real numbers satisfying the system of equations above, find the maximum possible value of \(a\).

Give your answer to 3 decimal places.

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