Question

If a = √2 + 1. Find the value of ( a - 1/a ) ^2

Answer 1

Answer:

$a=\sqrt2 +1\\\\\implies\dfrac{1}{a}=\dfrac{1}{\sqrt2 +1}\\\\\\\implies\dfrac{1}{a}=\dfrac{1}{\sqrt2 +1}\times\dfrac{\sqrt2 - 1}{\sqrt2 -1}\\\\\\\implies \dfrac{1}{a}=\dfrac{\sqrt2 -1}{(\sqrt2-1)(\sqrt2+1)}\\\\\\\implies \dfrac{1}{a}=\dfrac{\sqrt2-1}{2-1}$ 1/a = $\sqrt2 -1$

Subtracting 1/a from a :

= > a - 1/a

= > $\sqrt2$ + 1 - [ $\sqrt2$ - 1 ]

= > 1 + 1 = > 2

Hence,

= > ( a - 1 / a )^2

= > 2^2

= > 4

Required value is 4.