Question

If a = 2 + √3, then a + 1
a
= ?

Answer 1

Answer:

4 is your answer.

Appropriate question:-

•If a = 2 +√3 , then find a+1/a

Solution:-

First find :-

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

Rationalise them :-

$\tt \frac{1}{a} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \tt \frac{1}{a} = \frac{2 - \sqrt{3} }{ ({2})^{2} - {( \sqrt{3} })^{2} } \\ \\ \tt \frac{1}{a} = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \tt \frac{1}{a} = \frac{2 - \sqrt{3} }{1} \\ \\ \tt\frac{1}{a} = 2 - \sqrt{3}$

Now put the values in a+1/a ,

$\to \tt a + \frac{1}{a} = 2 + \sqrt{3} + (2 - \sqrt{3} ) \\ \\ \tt \to a + \frac{1}{a} = 2 + \sqrt{3} + 2 - \sqrt{3} \\ \\ \tt \to a + \frac{1}{a} = 4$

Hence solved ☺️

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Thanks for question