MathematicsIf x=22+7, then x+1xis

If $x = 2 \sqrt{2} + \sqrt{7}$ , then $x + \frac{1}{x}$ is

A
$2 \sqrt{2}$
B
$4 \sqrt{2}$
C
8
D
$\sqrt{7}$

Solution:

$\frac{1}{x} = \frac{1}{2 \sqrt{2} + \sqrt{7}} \times \frac{2 \sqrt{2} - \sqrt{7}}{2 \sqrt{2} - \sqrt{7}}$

$= \frac{2 \sqrt{2} - \sqrt{7}}{8 - 7} = 2 \sqrt{2} - 7$

$x + \frac{1}{x} = 2 \sqrt{2} + \sqrt{7} + 2 \sqrt{2} - \sqrt{7}$

$= 4 \sqrt{2}$

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