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If x^2+1/(x^2)=27 , find the values of e...

If `x^2+1/(x^2)=27` , find the values of each of the following: `x+1/x` (ii) `x-1/x` `x^2+1/(x^2)=(x+1//x)^2-2`
`(x+1//x)^2=27+2=29`
`(x+1//x)=sqrt29`
(ii) `(x-1/x)^2+2=x^2+1/(x^2)`
`(x-1//x)^2=27-2`
`(x-1//x)=5`

Text Solution

Verified by Experts

`x^2+1/(x^2)=(x+1//x)^2-2`
`(x+1//x)^2=27+2=29`
`(x+1//x)=sqrt29`
(ii) `(x-1/x)^2+2=x^2+1/(x^2)`
`(x-1//x)^2=27-2`
`(x-1//x)=5`
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