Question

if x = 3 − 2√2 then find the value of x + 1/x.



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Answer 1

$\fcolorbox{cyan}{orange}{Solutions:-}$

$\fcolorbox{cyan}{green}{Given:-}$

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

$\fcolorbox{cyan}{red}{To \: find:-}$

$(x + \frac{1}{x} )$

$\fcolorbox{cyan}{blue}{By \: the \: problem:-}$

$x = 3 - 2 \sqrt{2} \\ = > \frac{1}{x } = \frac{1}{3 - 2 \sqrt{2} } \\ \: multiply \: (3 + 2\sqrt{2} )\: in \: both \: numerator \: and \: denominator.\\ = \frac{1 \times (3 + 2\sqrt{2} )}{(3 - 2\sqrt{2}) (3 + 2\sqrt{2} } ) \\ = \frac{3 + 2\sqrt{2} }{9 - 8} \\ = \frac{3 + 2\sqrt{2} }{1} \\ = 3 + 2 \sqrt{2} \\ = > (x + \frac{1}{x} ) =(3 - 2\sqrt{2} + 3 + 2\sqrt{2} ) \\ = 6(ans)$

$\fcolorbox{cyan}{purple}{Answer:-}$

$6$