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प्रश्न
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
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उत्तर
Given that,`a = sqrt2` +1 hence `1/a`is given as
`1/a = 1/(sqrt2+1)`we are asked to find `a-1/a`
We know that rationalization factor for `sqrt2 +1` is `sqrt2 -1`. We will multiply each side of the given expression `1/(sqrt2+1)`by, `sqrt2-1` to get
`1/a = 1/(sqrt2+1) xx (sqrt2-1)/(sqrt2-1)`
` = (sqrt2 - 1) /((sqrt2^2) - (1)^2)`
`= (sqrt2 -1)/(2-1)`
`=sqrt2 - 1`
Therefore,
` a-1/a = sqrt2 +1- (sqrt2-1)`
` = sqrt2+1-sqrt2 +1`
`= 2`
Hence value of the given expression is 2.
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