Verified answer

[tex]\huge{\mathfrak{Answer: - }} \\ \bold{x - \frac{1}{x} = 3} \\ Squaring \: on \: both \: the \: sides \\ {(x - \frac{1}{x} )}^{2} = {(3)}^{2} \\ {(x)}^{2} + {( \frac{1}{x}) }^{2} - 2(x)( \frac{1}{x} ) = 9 \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 9 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 9 + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 11 \\ \boxed{\boxed{\bold{\large{ {x}^{2} + \frac{1}{ {x}^{2}} = 11}}}}[/tex]