Question

$if x = 2 + \sqrt{3} find = x + 1\x$
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Answer 1

Answer:

$The \: value \: of \: x + \frac{1}{x} \: is \: 4.$

Step-by-step explanation:

Given:

• x = 2+√3

To find:

• The value of $\fbox{${{x}\mathrm{{+}}\frac{1}{x}}$}$

Solution:

$x = 2 + \sqrt{3}$

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

$\frac{1}{x} = \frac{2 - \sqrt{3} }{(2 {)}^{2} -( \sqrt{3} {)}^{2} }$

$\frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3}$

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

Now, substitute the value

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

$\longrightarrow \: 2 + \sqrt{3} + 2 - \sqrt{3}$

$\longrightarrow2 + 2$

$\longrightarrow4$

$Hence \: the \: value \: of \: x + \frac{1}{x} \: is \: 4.$