If X 2 + 1 X 2 = 18 ; Find : X − 1 X - Mathematics

If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`

Sum

`x^2 + (1)/x^2 = 18`

Using `(x - 1/x)^2`

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

⇒ `(x - 1/x)^2`
= 18 - 2
= 16
⇒ `x - (1)/x`
= 4.

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