# Just 1+1

Algebra Level 2

Let $$x=1+1$$. If $$x$$ can be expressed in the form $$\frac{m}{n}$$, where $$m$$ and $$n$$ are coprime, positive integers, and $$2(m^{2}+n^{2}+2mn)=2^{a} \times 3^{b}$$, what is the value of $$a+b$$?

×