4 1 + 2 - 3 = - Vidyadip

MCQ

${4 \over {1 + \sqrt 2 - \sqrt 3 }} = $

✓
$2 + \sqrt 2 + \sqrt 6 $
B
$1 + \sqrt 2 + \sqrt 3 $
C
$3 + \sqrt 2 + \sqrt 3 $
D
None of these

✓

Answer

Correct option: A.

$2 + \sqrt 2 + \sqrt 6 $

a
(a) ${4 \over {1 + \sqrt 2 - \sqrt 3 }} = {{4\,(1 + \sqrt 2 + \sqrt 3 )} \over {{{(1 + \sqrt 2 )}^2} - 3}}$

$ = {{4(1 + \sqrt 2 + \sqrt 3 )} \over {3 + 2\sqrt 2 - 3}} + {{\sqrt 6 (\sqrt 3 - \sqrt 2 )} \over {3 - 2}}$

$ = \sqrt 2 (1 + \sqrt 2 + \sqrt 3 ) = 2 + \sqrt 2 + \sqrt 6 $.

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