<s>[INST] Solving $\sqrt{a-\sqrt{a+x}} = x$ Solve the equation
$$\sqrt{a-\sqrt{a+x}} = x$$
My approach:
Tried shifting the variables into different options, but couldn't get anything out of it. So, please help.
 [/INST] $$a-\sqrt{a+x}=x^2$$
$$a-x^2=\sqrt{a+x}$$
$$a+x=x^4-2ax^2+a^2$$
$$x^4-2ax^2-x+a^2-a=0$$
$$(x^2+x+1-a)(x^2-x-a)=0$$
You can factor the last expression by setting up $(x^2+px+q)(x^2+rx+s)=x^4-2ax^2-x+a^2-a$. And comparing the coefficient to find $p,q,r,s$.
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