Question

If x=3+√8 then find the value of x+1/x

Answer 1

given X=3+√8
put the value of x in eqn
x+1/x
3+√8+1/3+√8
(3+√8)(3+√8)/3+√8+1/3+√8
9+8+6√8/3+√8+1/3+√8
18+6√8/3+√8
rationalise it
18+6√8*3-√8/3+√8*3-√8
18+18√8-48/9-8
-30+18√8/1
-30+18√8

Answer 2

Here's your answer!!

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It's given that,

$= > x = 3 + \sqrt{8}$
So,

$= > \frac{1}{x} = \frac{1}{3 + \sqrt{8} }$

By rationalizing it ,we get :-

$= > \frac{1}{3 + \sqrt{8} } \times \frac{3 - \sqrt{8} }{3 - \sqrt{8} }$

$= > \frac{3 - \sqrt{8} }{ {(3)}^{2} - { (\sqrt{8} }^{2} )}$

$= > \frac{3 - \sqrt{8} }{9 - 8}$

Hence,


$= > \frac{1}{x} = 3 - \sqrt{8}$

Therefore,

$= > (x + \frac{1}{x} ) = 3 + \sqrt{8 } + 3 - \sqrt{8}$

$\sqrt{8} \: and \: - \sqrt{8} get \: cancelled$

Hence,


$= > (x + \frac{1}{x} ) = 6$

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Hope it helps you!! :)