If 4 + 3 3 (7 + 4 3 ) = a + b , then (a,b) = - Vidyadip

MCQ

If $\frac{{4 + 3\sqrt 3 }}{{\sqrt {(7 + 4\sqrt 3 )} }} = a + \sqrt b ,$ then $(a,b) = $

A
$(12,1)$
B
$(1, 12)$
✓
$(-1, 12)$
D
$(-12, 1)$

✓

Answer

Correct option: C.

$(-1, 12)$

c
(c) $\frac{{4 + 3\sqrt 3 }}{{\sqrt {7 + 4\sqrt 3 } }} = a + \sqrt b $

==> $\frac{{4 + 3\sqrt 3 }}{{2 + \sqrt 3 }} = a + \sqrt b $

==> $\frac{{(4 + 3\sqrt 3 )\,(2 - \sqrt 3 )}}{{(2 + \sqrt 3 )\,(2 - \sqrt 3 )}} = a + \sqrt b $

==> $ - 1 + 2\sqrt 3 = a + \sqrt b $

==> $ - 1 + \sqrt {12} = a + \sqrt b $; $\therefore $ $(a,\,b) = ( - 1,\,12)$.

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