Question

If a=√2+1,find the value of (a-1/a)^2

Answer 1

$Given : x = \sqrt{2} + 1$

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

$= \ \textgreater \ \frac{ \sqrt{2} - 1 }{(2)^2 - ( \sqrt{1} )^2}$

$= \ \textgreater \ \sqrt{2} - 1$

Now,

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

$= \ \textgreater \ 2$


Hence:

= > (a - 1/a)^2 = (2)^2

                       = 4.




Therefore the value of (a - 1/a)^2 = 4.


Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks