If f(x) = frac{1}{{√ {x + 2√ {2x - 4} } }} + frac{1}{{√ {x - 2√ {2x - 4} } }} for x > 2 ,

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1.Relation and Function

easy

If $f(x) = \frac{1}{{\sqrt {x + 2\sqrt {2x - 4} } }} + \frac{1}{{\sqrt {x - 2\sqrt {2x - 4} } }}$ for $x > 2$, then $f(11) = $

A

$7/6$

B

$5/6$

C

$6/7$

D

$5/7$

Solution

(c) $f(x) = \frac{1}{{\sqrt {x + 2\sqrt {2x – 4} } }} + \frac{1}{{\sqrt {x – 2\sqrt {2x – 4} } }}$

$f(11) = \frac{1}{{\sqrt {11 + 2\sqrt {18} } }} + \frac{1}{{\sqrt {11 – 2\sqrt {18} } }}$

$ = \frac{1}{{3 + \sqrt 2 }} + \frac{1}{{3 – \sqrt 2 }} = \frac{{3 – \sqrt 2 }}{7} + \frac{{3 + \sqrt 2 }}{7} = \frac{6}{7}$.

Standard 12

Mathematics

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