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STD 11 - 4.2 Quadratic equations and inequations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.2 Quadratic equations and inequations4 Marks
Question
If $x = \sqrt {7 + 4\sqrt 3 } ,$ then $x + \frac{1}{x} = $
✓

Answer

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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