Question

If `x^2 + 1/x^2 = 27`. Then find `x-1/x` ?

If `x^2 + 1/x^2 = 27`. Then find `x-1/x`

Answer 1

`x-1/x = +-5`

Explanation:

just expand, rearrange n substitute,!
`(x-1/x)^2`

`=x^2 -2*x*1/x +(1/x)^2`

`=x^2 -2+(1/x)^2`

`=x^2+1/x^2-2`

since we have the value of `x^2+1/x^2` as `27`,

`=27-2`

`=25`

`=>(x-1/x)^2 = 25`

`=>x-1/x = +-5`

-Sahar

Answer 2

`x-1/x=+-5`

Explanation:

`"note that "(x-1/x)^2=x^2-2+1/x^2`

`rArrx^2-2+1/x^2=27-2=25`

`rArr(x-1/x)^2=25`

`color(blue)"take the square root of both sides"`

`rArrx-1/x=+-5larrcolor(blue)"note plus or minus"`