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प्रश्न
If x = \[\sqrt{5} + 2\],then \[x - \frac{1}{x}\] equals
पर्याय
\[2\sqrt{5}\]
4
2
\[\sqrt{5}\]
उत्तर
Given that. `x=sqrt5 +2 ` Hence `1/x`is given as
`1/x = 1/(sqrt5+2)`.We need to find `x - 1/x`
We know that rationalization factor for `sqrt5+2` is`sqrt5-2`. We will multiply numerator and denominator of the given expression\`1/(sqrt5 +2)` by`sqrt5 - 2`, to get
`1/x = 1/(sqrt5+2 ) xx (sqrt5 - 2)/(sqrt5 -2)`
` = (sqrt 5-2)/((sqrt5)^2 - (2)^2 )`
`=(sqrt5 -2)/(5-4)`
` = sqrt5 - 2`
Therefore,
`x - 1/x=sqrt5 +2 -(sqrt5 - 2)`
`= sqrt5 +2 - sqrt5 +2`
` = 2+2`
` = 4`
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