Question

Let \(f\) be a function such that \(\sqrt {x - \sqrt { x + f(x) } } = f(x) , \) for \(x > 1\). In that domain, \(f(x)\) has the form \(\frac{a+\sqrt{cx+d}}{b},\) where \(a,b,c,d\) are integers and \(a,b\) are relatively prime. Find \(a+b+c+d.\)