SSC CGL 3 Sep 2016 Paper

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Question : 65 of 100

Marks: +1, -0

If x = 2 +

√3

, then the value of

{x^2-x+1}/{x^2+x+1}

is :

$2/3$
$3/4$
$4/5$
$3/5$

Solution:

x = 2 +

√3

∴

x^2

=

(2+√3)^2

= 4 + 3 +

4√3

= 7 +

4√3

∴

{x^2-x+1}/{x^2+x+1}

=

{74√3-(2+√3)+1}/{74√3+2+√3+1}

=

{8+4√3-2-√3}/{10+5√3}

=

{6+3√3}/{10+5√3}

=

{3(2+√3)}/{5(2+√3)}

=

3/5

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