If $$x + \frac{1}{x} = 3$$, then $$x^2 + \frac{1}{x^2}$$ is:

Correct option is D

Given:

​$$x + \frac{1}{x} = 3$$​​

Formula Used:

​$$(a+b)^2 = a^2 + b^2 +2ab$$​​

Solution:

​$$x + \frac{1}{x} = 3$$​​

Squaring both sides

​$$\left(x + \frac{1}{x}\right) = (3)^2$$​​

​$$x^2 + \left(\frac{1}{x} \right)^2 + 2(x)\left(\frac{1}{x}\right) = 9$$​​

​$$x^2 + \frac{1}{x^2} + 2= 9$$​​

​$$x^2 + \frac{1}{x^2} = 9-2 = 7$$​​