SSC CGL 5 Aug 2017 Shift 1 Paper

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Question : 62 of 100

Marks: +1, -0

If

x = 2 + √3,

then what is the value of

√{2x }+ 1/√{2x } = ?

$2√3$
$3√3$
$(3√3 + 1 )/2$
$2 √3 + 1$

Solution:

x = 2 + √3

⇒

2x=2(2+√3)

On taking square root of both sides,

√{2x}=√{2(2+√3)}=√{4 +2√3}

= √{1+3+2√3}=√(1+√3)^2

=1+√3

and

1/√{2x }=1/{1+√3} ×{1-√3}/{1-√3}

{1-√3}/{1-3}={-1√3}/2

∴

√{2x}+1/√{2x}=1+√3+[-1+√3]/2

={2+2√3-1+√3}/2

={1+3√3}/2

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