SSC CGL 8 Aug 2017 Shift 1 Paper

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Question : 62 of 100

Marks: +1, -0

If

x = 6 + 2√6

, then what is the value of

√{x-1}+1/√{x-1}

?

$2√3$
$3√2$
$2√2$
$3√3$

Solution:

x = 6 + 2√6

On subtracting 1 from both sides,

x - 1 = 6 + 2√6 - 1

⇒

x-1 = 5 + 2√6

⇒

√{x-1}=√{5+2√6}

=√(√3+√2)^2=√3+√2

and

1/√{x-1}=1/{√3+√2}× {√3-√2}/{√3-√2}

=√3-√2

∴

√{x-1}+1/√{x-1}

=√3+√2+√3-√2

=2√3

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