Question

If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].

Answer 1

We have to find the value of  `a - 1/a`

Given  `a^2+1/a^2 = 102`

Using identity  `(x-y)^2 = x^2 +y^2 - 2xy`

Here  `x=a,y = 1/a`

`(a-1/a )^2 = a^2 + (1/a)^2 - 2xx a xx 1/a`

`(a-1/a )^2 = a^2 + 1/a^2 - 2xx a xx 1/a`

By substituting  `a^2 + 1/a^2 = 102` we get 

                `(a-1/a)^2 = 102 -2`

                `(a-1/a)^2 = 100`

`(a-1/a )(a-1/a) = 10 xx 10`

                   `(a-1/a) = 10`

Hence the value of  `a-1/a` is 10.