R.M.S>.A.M (you may use the fact)

Algebra Level 4

In a right angled triangle, \(A\) and \(B\) denote the lenghts of the medians that belong to the legs of the triangle, and the length of the median belonging to the hypotenuse is \(C\). Find the maximum value of the expression \(\dfrac{A+B}{C}\), the answer is of the form \(\sqrt{X}\) and so find \(X\).

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