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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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Knowledge Check

  • If x^2+1/x^2=27 ,then value of x+1/x is

    A
    9
    B
    29
    C
    `sqrt29`
    D
    3

  • If (x + 1//x)^3 = 27 then find the value of x^2 + 1//x^2 .

    A
    11
    B
    9
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    7
    D
    15

  • If x ^(2) + 1//x ^(2) = 2, then the value of (x - (1)/(x)) is

    A
    `-2`
    B
    0
    C
    1
    D
    `-1`

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