If $$(x+\frac{1}{x})=7$$​, then $$(x-\frac{1}{x})$$​ is equal to:

Correct option is C

Given:

​$$\left( x + \frac{1}{x} \right) = 7$$​

We are required to find the value of

​$$\left( x - \frac{1}{x} \right).$$​​

Concept Used:
We will use the identity:

$$\left( x + \frac{1}{x} \right)^2 - \left( x- \frac{1}{x} \right)^2 = 4$$​

Solution:

​$$\left( x + \frac{1}{x} \right)^2 - \left( x - \frac{1}{x} \right)^2 = 4$$​

Squaring both sides of $$\left( x + \frac{1}{x} \right) = 7$$​, we get:

​​$$\left( x - \frac{1}{x} \right)^2 = 49 - 4 = 45$$

$$\left( x - \frac{1}{x} \right) =3\sqrt 5$$​​​