Find the roots of $$x^{-4} - 10x^{-2} + 9 = 0$$​​

Correct option is D

Given:

​$$x^{-4} - 10x^{-2} + 9 = 0$$​​

Solution:

Let y = $$x^{-2}$$​, so the equation becomes:

y² - 10y + 9 = 0

y² - 1y - 9y + 9 = 0 

y( y - 1) - 9(y - 1) = 0

(y - 1)(y - 9) = 0

y = 1 and 9 

Substituting back y = $$x^{-2}$$​:

For y = 1, $$x^{-2}$$​ = 1, hence x = $$\pm$$​1

For y = 9, $$x^{-2}$$​ = 9, hence x = $$\pm \frac{1}{3}$$​​