A cool algebra problem....

Algebra Level pending

If \(a,b\) are positive real numbers such that \(a - b = 2\) , then find the smallest value of the constant \(L\) for which the condition

\((x^2 + ax)^{1/2} - (x^2 + bx)^{1/2} < L\) holds for all \(x>0\).

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