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