<s>[INST] Find $x-\sqrt{7x}$ given that $x - \sqrt{\frac7x}=8$ 
If $ x - \sqrt{\frac{7}{x}}=8$ then $x-\sqrt{7x}=\text{?}$ 

I used some ways, but couldn't get the right form :) by the way, the answer is $1$.
Thanks in advance.
 [/INST] \begin{eqnarray*}
x-\sqrt{\frac{7}{x}}=8 \\
x-8 =\sqrt{\frac{7}{x}}
\end{eqnarray*}
Now square both sides and multiply by $x$
\begin{eqnarray*}
x^2-16x+64=\frac{7}{x} \\
x^3-16x^2+64x-7=0 \\
(x-7)(x^2-9x+1)=0
\end{eqnarray*}
Now assume $x$ does not equal $7$ and taking the positive square root will give
\begin{eqnarray*}
x^2-9x+1=0 \\
x^2-2x+1= 7x \\
(x-1)^2 =7x \\
x-1 = \sqrt{7x} \\
x-\sqrt{7x}= \color{red}{1}.
\end{eqnarray*}
</s>