<s>[INST] How do I solve an equation with three terms, with the unknown inside a square root, inside a third root, in two of them? The equation is $$\\ \sqrt[3]{\sqrt{a}+b}+\sqrt[3]{-\sqrt{a}+b}=k.$$
How do I find$\ a$? 
 [/INST] $$k=(b+c)^{1/3}+(b-c)^{1/3}$$ where $c=\sqrt a$. We use $(x+y)^3=x^3+y^3+3xy(x+y)$. 
$$k^3=b+c+b-c+3(b^2-c^2)^{1/3}k=2b+3k(b^2-c^2)^{1/3}$$ 
Now subtract $2b$, divide by $3k$, cube, subtract from $b^2$, and you have $c^2$, which is $a$. 
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