Question

If x= (3-√13)/2 what is the value of x^2 + 1/x^2 ????

Answer 1

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$\star \: \underline \blue{Solution} \blue{ : -}$

$x = \frac{3 - \sqrt{13} }{2}$

$\longrightarrow \: x = \frac{(3 - \sqrt{13})(3 + \sqrt{13}) }{2(3 + \sqrt{13}) }$

$\longrightarrow \: x = \frac{9 - 13}{2(3 + \sqrt{13}) }$

$\longrightarrow \: x = \frac{ - 4} {2(3 + \sqrt{13}) }$

$\longrightarrow \: \frac{1}{x} = - \frac{3 + \sqrt{13} }{2}$

$\bold{adding \: x \: and \: \frac{1}{x} } \\ x + \frac{1}{x} \\ = \frac{3 - \sqrt{13} }{2} - \frac{3 + \sqrt{13} }{2 } \\ = \frac{3 - \sqrt{13} - 3 - \sqrt{13} }{2} \\ = \boxed {\mathfrak{{ - 2 \sqrt{13} }}}$

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