Ununderstandable alternate form of a function

Question

Helo, i've a doubt about this function: $$f(x)=\frac{\sqrt{16 - x^2} - x\sqrt{46 + 25( \sqrt[4]2})}{x\sqrt{(46 + 25 (\sqrt[4]2)}}$$
I want to find the roots of $f(x)$ for $f(x)=0$, Wolfram alpha has given me this results:

Alternate form assuming $x$ is positive: $$x=\sqrt{\frac{16}{47+25\sqrt[4]2}}$$
I don't have idea where tath came from, can you explain me please?

Answer 1

Because for positive $x$ we obtain: $$\sqrt{16-x^2}=x\sqrt{46+25\sqrt[4]2}$$ or $$16-x^2=x^2(46+25\sqrt[4]2)$$ or $$x^2=\frac{16}{47+25\sqrt[4]2}$$