SSC CGL 30 Aug 2015 Paper

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Question : 109 of 200

Marks: +1, -0

If

{√{a+2b}+√{a-2b}}/{√{a+2b}-√{a-2b}}

=

√3

, then a : b is equal to

2 : $√3$
$√3$ : 4
$√3$ : 2
4 : $√3$

Solution:

{√{a+2b}+√{a-2b}}/{√{a+2b}-√{a-2b}}

=

√3

By componendo and dividendo,

{√{a+2b}+√{a-2b}+√{a+2b}-√{a-2b}}/{√{a+2b}+√{a-2b}-√{a+2b}+√{a-2b}}

=

{√3+1}/{√3-1}

⇒

√{a+2b}/√{a-2b}

=

{√3+1}/{√3-1}

On squaring,

{a+2b}/{a-2b}

=

{3+1+2√3}/{3+1-2√3}

=

{4+2√3}/{4-2√3}

⇒

{a+2b}/{a-2b}

=

{2+√3}/{2-√3}

By componendo and dividendo,

{a+2b+a-2b}/{a+2b-a+2b}

=

{2+√3+2-√3}/{2+√3+2+√3}

⇒

{2a}/{4b}

=

4/{2√3}

⇒

a/{2b}

=

2/√3

⇒

a/b

=

4/√3

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