Question

If a=2+√3 , then find the value of a-1/a.

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Answer 1

Given

$a = 2 + \sqrt{3}$

Substituting, we get,

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

Rationalizing the denominator,

$\bold{\frac{1+\sqrt{3} }{2+\sqrt{3} } * \frac{2-\sqrt{3} }{2-\sqrt{3} } }$

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

$\bold{\frac{-1+\sqrt{3} }{1} }$

$\boxed{\boxed{\bold{ \sqrt{3}-1} }}$

                                                   

Answer 2

√3 - 1

2√3

Step-by-step explanation:

Given:

a = 2 +√3

To find:

It's not clearly mentioned that ,

$\frac{a - 1}{a} .........(i) \\ \\ \: \: or \\ \\ \: a \: \: - \frac{1}{a} .......(ii)$

Solution:

In (i),

Substituting the value I get ,

$\frac{2 + \sqrt{3} - 1 }{2 + \sqrt{3} } \\ \\ \frac{1 + \sqrt{3} }{2 + \sqrt{3} } \\ \: \\ [Rationalizing \: \: \: the \: \: \: denominator] \: \\ \\</p><p>\frac{(1 + \sqrt{3} )(2 - \sqrt{3} )}{(2 + \sqrt{3} )(2 - \sqrt{3} )} \\ \\ \frac{2 - \sqrt{3} + 2 \sqrt{3} - 3}{ {(2)}^{2} - {( \sqrt{3}) }^{2} } \\ \\ \frac{ \sqrt{3} - 1 }{1} \\ \\ \sqrt{3} - 1$

So, (i) is √3 - 1.

In (ii),

See in the attachment.