# Functional System of Equation

Algebra Level 5

Let $$f(x)=x-\dfrac{1}{x}$$.

If $$(a_1,b_1)\cdots (a_n,b_n)$$ are the solutions to the system of equations

$\left\{\begin{array}{l}f(a)+f(b)=f(ab)\\ a=f(b)\end{array}\right.$

then the value of $\sum_{i=1}^n|a_i|+|b_i|$ can be expressed as $\sqrt{a}+\sqrt{b}+\sqrt{c}$ for positive integers $$a,b,c$$.

Find $$a+b+c$$.

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