If $$x^2+\frac{1}{x^2}=10$$​, then what is the value of $$x^4+\frac{1}{x^4}$$​ ?

Correct option is C

Given:

$$x^2+\frac{1}{x^2}=10$$,  ​ 

$$x^4+\frac{1}{x^4}$$

Formula Used:

$$\text{To find } x^4 + \frac{1}{x^4}, \text{ we use the identity:} \\x^4 + \frac{1}{x^4} = \left(x^2 + \frac{1}{x^2}\right)^2 - 2$$​

Solution:

$$\left(x^2 + \frac{1}{x^2}\right)^2 = 10^2 = 100 \\\text{Now,} \\x^4 + \frac{1}{x^4} = 100 - 2 = 98$$

​Final Answer:
(c) 98