SSC CGL 5 Aug 2017 Shift 1 Paper

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Question : 61 of 100

Marks: +1, -0

If

x = {2+√3}/{2-√3}

, then what is the value of

x +1/x

?

14
$8√3$
0
18

Solution:

x = {2+√3}/{2-√3}

= {2+√3}/{2-√3} × {2+√3}/{2+√3}

= (2+√3)^2/{(2)^2-(√3)^2}

={4+3+4√3}/{4-3}=7+4√3

and

1/x=1/{7+4√3} ×{7-4√3}/{7-4√3}

=7-4√3

∴

x +1/x=7+4√3+7-4√3

=14

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