If $$x+\frac{1}{x}=6$$​, then value of $$x^2+\frac{1}{x^2}$$​ is:

Correct option is D

Given:

​$$x + \frac{1}{x} = 6$$​

Formula Used:

​$$(x + \frac{1}{x})^2 = x^2 + \frac{1}{x^2} + 2$$​

Solution:

Given:

​$$x + \frac{1}{x} = 6$$​​

Now square both sides:

​$$(x + \frac{1}{x})^2 = 6^2 = 36$$​​

​$$x^2 + \frac{1}{x^2} + 2 = 36$$​​

​$$x^2 + \frac{1}{x^2} = 36 - 2 = 34$$​