Question

if x=3+2√2, then find x+1/x?​

Answer 1

$\bf\large\underline\blue{Question:-}$

• If $x=3+2\sqrt{2}$, find the value of $x+\frac{1}{x}$

$\bf\large\underline\blue{Solution:-}$

$x = 3 + 2\sqrt{2}$

$\bf\small\underline\blue{Therefore,}$

$\frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} }$

Now, we have to rationalize the denominator.

Rationalizing means to remove all the surds from the denominator.

$\bf\small\underline\blue{Therefore,}$

$\frac{1}{3 + 2 \sqrt{2} }$

$= \frac{1}{(3 + 2 \sqrt{2} )} \times \frac{(3 - 2 \sqrt{2} )}{(3 - 2\sqrt{2} )}$

$= \frac{3 - 2 \sqrt{2} }{ {(3)}^{2} - {(2 \sqrt{2}) }^{2} }$

$= \frac{3 - 2 \sqrt{2} }{9 - 8}$

$= \frac{3 - 2 \sqrt{2} }{1}$

$= 3 - 2 \sqrt{2}$

$\bf\small\underline\blue{Therefore}$

$x + \frac{1}{x} = 3 + 2 \sqrt{2} + 3 - 2 \sqrt{2}$

$= 3 + 3 + \cancel{2 \sqrt{2} } - \cancel{2 \sqrt{2} }$

$= 6$

$\bf\small\underline\blue{Therefore,}$

$x + \frac{1}{x} = 6$

$\bf\large\underline\blue{Answer:-}$

• The value of $x + \frac{1}{x}$ is $6$

Answer 2

1. Step-by-step explanation:

i hope it helps u