Question

If a=√2+1, Find the value of a-1/a

-1

1

2

-2​

Answer 1

$\huge\fbox\red{Solution:}$

Given:

a = √2 + 1

1/a = 1/(√2 + 1)

= 1/(√2 + 1) x (√2 - 1)/(√2 - 1)

= (√2 - 1)/ ((√2)^2 - (1)^2)

= (√2 - 1)/1

= √2 - 1

Now,

a - 1/a = (√2 + 1) - (√2 - 1)

= 2