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4-2.Quadratic Equations and Inequations
medium
જો $x = \sqrt {7 + 4\sqrt 3 } $, હોય તો $, x + \frac{1}{x} = ......$
A
$4$
B
$6$
C
$3$
D
$2$
Solution
$\,x = \sqrt {7 + 4\sqrt 3 } $ સમીકરણ આપેલ છે.
$\therefore \,\,\frac{1}{x} = \frac{1}{{\sqrt {7 + 4\sqrt 3 } }} = \frac{{\sqrt {7 – 4\sqrt 3 } }}{{\sqrt {7 + 4\sqrt 3 } .\sqrt {7 – 4\sqrt 3 } }}$
$ = \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$
Standard 11
Mathematics
