<s>[INST] 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...
 [/INST] Divide by $x$:
$$\sqrt{\frac1x-\frac1{x^3}}+\sqrt{\frac1{x^2}-\frac1{x^3}}=1$$
Change $t=1/x$:
$$\sqrt{t-t^3}+\sqrt{t^2-t^3}=1$$
Square and rearrange:
$$2\sqrt{t^3-t^4-t^5+t^6}=t+t^2-2t^3-1$$
Square and rearrange again:
$$4t^6-4t^5-4t^4+4t^3=4t^6-4t^5-3t^4+6t^3-t^2-2t+1$$
Finally we get
$$t^4+2t^3-t^2-2t+1=0$$
That is,
$$(t^2+t-1)^2=0$$
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