Question

Find the roots of the following equation:-

x - $\frac{1}{x}$ = 3, x ≠ 0

Answer 1

Refer the attached picture.

Answer 2

$\bold{ \underline{ \red{SOLUTION \: \: }}}$ ➡

$\bold{x - \frac{1}{x} } = 3 \\ \\ \bold{ = > \frac{x {}^{2} - 1}{x} = 3} \\ \\ \bold{ = > x {}^{2} - 1 = 3x} \\ \\ \bold{ = > x {}^{2} - 3x - 1= 0 }$

$\bold{Here , } \\ \\ \: \: \: \: \: \: \: \bold{a = 1} \\ \: \: \: \: \: \: \: \bold{b = - 3} \\ \: \: \: \: \: \: \: \bold{c = - 1}$

$\bold{So , } \\ \\ \bold{x = \frac{ - b ± \sqrt{b {}^{2} - 4ac} }{2a} } \\ \\ \bold{ = \frac{ - 3 ± \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 1)} }{2 \times 1} } \\ \\ \bold{ = \frac{ - 3 ± \sqrt{9 + 4} }{2} } \\ \\ \bold{ = \frac{ - 3 ± \sqrt{13} }{2} }$

$\bold{Hence,} \\ \\ \bold{x = \frac{ - 3 + \sqrt{13} }{2} \: \: \: or \: \: \: \: x = \frac{ - 3 - \sqrt{13} }{2} }$

$\bold{ \underline{ \red{ANSWER \: }}}$ ➡

$\bold{The \: \: roots \: \: are : \: \: \: \: \: \frac{ - 3 + \sqrt{13} }{2} \: \: \:, \: \: \: \: \frac{ - 3 - \sqrt{13} }{2} } \: \: \: \: \: \: \:$

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✝ $\mathfrak{\red{THANKS...}}$ ✝