<s>[INST] Evaluate $x+4/x$ when $x$ is a solution of $x-6/\sqrt{x}=11$ I have a question that I see in a math text.
I asked to my teacher but she couldn't find the solution, too. 
If 
$$x - \frac{6}{\sqrt{x}}=11,$$
then to what is equal
$$x + \frac{4}{x}\text{ ?}$$
 [/INST] AS $x-\frac{6}{\sqrt{x}}-11=(\sqrt{x}+3)(\sqrt{x}-\frac{2}{\sqrt{x}}-3)$, so from $x-\frac{6}{\sqrt{x}}=11$ and $\sqrt{x}\geq0$, we can obtain that $\sqrt{x}-\frac{2}{\sqrt{x}}=3$, squaring at both sides, i.e. $(\sqrt{x}-\frac{2}{\sqrt{x}})^{2}=x+\frac{4}{x}-4=9$, so $x+\frac{4}{x}=13$.
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