Quadratic equation find all the real values of $x$ Find all real values of $x$ such that 
$\sqrt{x - \frac{1}{x}} + \sqrt{1 - \frac{1}{x}} = x$
I tried sq both sides by taking 1 in RHS but it didn't worked out well...

HINT: after squaring one times we get
$$2\sqrt{x-\frac{1}{x}}\sqrt{1-\frac{1}{x}}=x^2-x+\frac{2}{x}-1$$
can you finish this?
squaring this one more times we get
$$4\left(x-\frac{1}{x}\right)\left(1-\frac{1}{x}\right)=\left(x^2-x+\frac{2}{x}-1\right)^2$$
expanding the left Hand side we obtain $$4\,x-4-4\,{x}^{-1}+4\,{x}^{-2}$$ and the right Hand side is given by $${x}^{4}-2\,{x}^{3}+6\,x-{x}^{2}-3+4\,{x}^{-2}-4\,{x}^{-1}$$ have you got this?
Bringung all together we obtain this equation
$$0=x^4-2x^3-x^2+2x+1$$
