Question

if a =2+√3 then find (a +1/a)​

Answer 1

Step-by-step explanation:

$a = 2 + \sqrt{3}$

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

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

$\frac{2 - \sqrt{3} }{4 - 3}$

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

$= 2 - \sqrt{3}$

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

$a + \frac{1}{a} = 4$

THEREFORE, $a + \frac{1}{a} = 4$

Answer 2

Answer:

Given ;

$a = 2 + \sqrt{3}$

$to \: find \: : \: a + \dfrac{1}{a}$

Substituting the value of a ,

$\hookrightarrow \: 2 + \sqrt{3} + \dfrac{1}{2 + \sqrt{3} }$

$\hookrightarrow \: \dfrac{ 4 + 3 + 4 \sqrt{3} + 1} {2 + \sqrt{3} }$

$\hookrightarrow \: \dfrac{8 + 4 \sqrt{3} }{2 + \sqrt{3} }$

$\hookrightarrow \: \dfrac{4(2 + \sqrt{3}) }{2 + \sqrt{3} }$

Cancelling 2 + √3

$\hookrightarrow \: \huge 4$

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hope it helps....!