<s>[INST] $ 1 + \sqrt{1 - \sqrt{x^4-x^2}} = x$ can be written in the form $\frac{a}{b}$, find $a+b$. The solution to the equation 
$$1 + \sqrt{1 - \sqrt{x^4-x^2}} = x$$
 can be written in the form $\frac{a}{b}$ where $a$ and $b$ are coprime positive integers. Find $a+b$.
 [/INST] I assume the question is not a live problem anymore. What you can do to solve this is just solving for $x$. So assume $x$ is a solution, then $\sqrt{1-\sqrt{x^4-x^2}}=x-1$, so $1-\sqrt{x^4-x^2}=(x-1)^2$. Continuing like this you will get to $-4x^3+5x^2=0$. This has two solutions, but one of the solutions is not a solution to the original equation, an excellent example that squaring will in general not yield to an equivalent equation.
</s>