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If x+1/x=6 , find x^2+1/(x^2) (ii) x^...

If `x+1/x=6 ` , find `x^2+1/(x^2)` (ii) `x^4+1/(x^4)` `(x+1//x)^2=6`
`x^2+1/(x^2)+2=36`
`x^2+1/(x^2)=36-2`
`x^2+1/(x^2)=34`
(ii) `(x^2+1/x^2)^2=x^4+1/(x^4)+2`
`(x^4+1/x^4)=34^2-2`
`x^4+1/(x^4)=1154`

Text Solution

Verified by Experts

`(x+1//x)^2=6`
`x^2+1/(x^2)+2=36`
`x^2+1/(x^2)=36-2`
`x^2+1/(x^2)=34`
(ii)`(x^2+1/x^2)^2=x^4+1/(x^4)+2`
`(x^4+1/x^4)=34^2-2`
`x^4+1/(x^4)=1154`
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