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Solve the following quadratic equation by factorization:
$x\ –\ \frac{1}{x}\ =\ 3,\ x\ ≠\ 0$
Given:
Given quadratic equation is $x\ –\ \frac{1}{x}\ =\ 3,\ x\ ≠\ 0$.
To do:
We have to solve the given quadratic equation by factorization.
Solution:
$x\ –\ \frac{1}{x}\ =\ 3$ can be written as,
$x(x-\frac{1}{x}=x(3)$ (Multiply by $x$ on both sides)
$x^2-1=3x$
$x^2-3x-1=0$
$ \begin{array}{l}
x=\frac{-( -3) \pm \sqrt{( -3)^{2} -4( 1)( -1)}}{2( 1)}\\
\\
x=\frac{3\pm \sqrt{9+4}}{2}\\
\\
x=\frac{3\pm \sqrt{13}}{2}\\
\\
x=\frac{3+\sqrt{13}}{2} \ or\ x=\frac{3-\sqrt{13}}{2}
\end{array}$
x=\frac{-( -3) \pm \sqrt{( -3)^{2} -4( 1)( -1)}}{2( 1)}\\
\\
x=\frac{3\pm \sqrt{9+4}}{2}\\
\\
x=\frac{3\pm \sqrt{13}}{2}\\
\\
x=\frac{3+\sqrt{13}}{2} \ or\ x=\frac{3-\sqrt{13}}{2}
\end{array}$
The roots of the given quadratic equation are $\frac{3+\sqrt{13}}{2}$ and $\frac{3-\sqrt{13}}{2}$. 
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