Question

if a = 2-√3
then find the value of a-1/a​

Answer 1

Answer:

$a = 2 - \sqrt{3} \\ \frac{1}{a } = \frac{1}{2 - \sqrt{3} } \\ \: \: = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{2 + \sqrt{3} }{4 - 3} = \frac{2 + \sqrt{3} }{1} = 2 + \sqrt{3} \\ therefore \: \: a - \frac{1}{a } = 2 - \sqrt{3} - 2 - \sqrt{3} \\ = - 2 \sqrt{3}$

Answer 2

Answer:

Answer:

\begin{gathered}a = 2 - \sqrt{3} \\ \frac{1}{a } = \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} \\ therefore \: \: a - \frac{1}{a } = 2 - \sqrt{3} - 2 - \sqrt{3} \\ = - 2 \sqrt{3}\end{gathered}

a=2−

3

a

1

=

2−

3

1

=

2−

3

1

×

2+

3

2+

3

=

4−3

2+

3

=

1

2+

3

=2+

3

thereforea−

a

1

=2−

3

−2−

3

=−2

3