If a = √ 2+1, then find (a-1/a) ^2

Answer: (a-1/a) ^2 = 4 where a = √2 + 1

Step-by-step explanation:

Given a = √2 + 1

Now a - 1 / a = (√2+1) - 1 / (√2+1)

Multiplying and dividing by √2+1

= ((√2+1) ² - 1) / (√2+1)

= (2+1 + 2√2-1) / (√2+1) [ (a+b) ² = a² + b² + 2ab]

= (2 + 2√2) / (√2+1)

= 2 (√2+1) / (√2+1)

=2

Now we have to find (a-1/a) ^2

i. e. 2^2

=2²

=4

So (a-1/a) ^2 = 4

The correct answer is 4.