Infinite nested roots. Answer 2016 or maybe not? Try it.

Algebra Level 3

There is a function

\(f\left( x \right) =\sqrt { x+\sqrt { x+\sqrt { x+\sqrt { x+.... } } } } \)

and there are two numbers, \(a\) and \(b\), both integers. It is known that:

1.\( f(a) \times\ f(b) = 999 \)

2.\( f(a) + f(b) = 64 \)

But, unfortunately a + b is uknown. Let change that!

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