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4.2 Quadratic equations and inequations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.2 Quadratic equations and inequations1 Mark
MCQ
If $x = \sqrt {7 + 4\sqrt 3 } ,$ then $x + \frac{1}{x} = $
  • ✓
    $4$
  • B
    $6$
  • C
    $3$
  • D
    $2$
✓

Answer

Correct option: A.
$4$
a
(a) We have $x = \sqrt {7 + 4\sqrt 3 } $

$\therefore$ $\frac{1}{x} = \frac{1}{{\sqrt {7 + 4\sqrt 3 } }} = \frac{{\sqrt {7 - 4\sqrt 3 } }}{{\sqrt {7 + 4\sqrt 3 } .\sqrt {7 - 4\sqrt 3 } }} = \sqrt {7 - 4\sqrt 3 } $

$\therefore$ $x + \frac{1}{x} = \sqrt {7 + 4\sqrt 3 } + \sqrt {7 - 4\sqrt 3 } $

$ = (\sqrt 3 + 2) + (2 - \sqrt 3 ) = 4$.

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