Question

If a = √2 - 1, then find the value of   2a – 1/a. ​

Answer 1

$\huge\sf\green{Answer :}$

√2 - 3

$\huge\sf\pink{Explanation :}$

Given :

a = √2 - 1

$\: \: \: \: \:$

To Find :

$2a \: - \frac{1}{a}$

$\: \: \: \: \:$

Solution :

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

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

➣$\frac{1}{a} = \frac{ \sqrt{2} + 1}{ ({ \sqrt{2} })^{2} - {(1)}^{2} }$

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

➣$\frac{1}{a} = \sqrt{2} + 1$

$\: \: \: \: \:$

$2a \: - \frac{1}{a}$ :

➣$2a \: - \frac{1}{a} = 2( \sqrt{2} \: - \: 1) - ( \sqrt{2} \: + \: 1)$

➣$2a \: - \frac{1}{a} = 2 \sqrt{2} - 2 - \sqrt{2} - 1$

➣$2a \: - \frac{1}{a} = \sqrt{2} - 3$