Question

if x = 2+√3 find the value of x+1/x​

Answer 1

Answer:

76

Step-by-step explanation:

Answer 2

Hey mate!

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Given :

$x = 2 + \sqrt{3}$

To find :

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

Solution :

$\begin{gathered}x = 2 + \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{(2) {}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 - \sqrt{ 3} \end{gathered}$

Now,

$\begin{gathered}x + \frac{1}{x} \\ \\ \implies 2 + \cancel{\sqrt{3}} + 2 - \cancel{ \sqrt{3}} \\ \\ \implies 2 + 2 \\ \\ \implies 4\end{gathered}$

Hence,

The answer is 4.

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Thanks for the question !

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