Question

if x=(2+√5)find the value of x in x2+1/x2

Answer 1

$x = (2 + \sqrt{5} ) \\ {x}^{2} = ( {2 + \sqrt{5} )}^{2} = 4 + 5 + 4 \sqrt{5} \\ = 9 + 4 \sqrt{5}$
$\frac{1}{ {x}^{2} } = \frac{1}{9 + 4 \sqrt{5} } \\ = \frac{(9 - 4 \sqrt{5} )}{(9 + 4 \sqrt{5})(9 - 4 \sqrt{5} ) } \\ = \frac{(9 - 4 \sqrt{5} )}{81 - 80} \\ = 9 - 4 \sqrt{5} \\ {x}^{2} + \frac{1}{ {x}^{2} } = 9 + 4 \sqrt{5} + 9 - 4 \sqrt{5} \\ = 18 \: \: \: ans$

Answer 2

hey friend ,


I had answered your same question earlier,

you can refer to this link:

https://brainly.in/question/4325976

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thanks!