Question

If x²+ 1/x²= 23, find the value of x²- 1/x²​

Answer 1

, x^2+1/x^2 = 23 and hence, (x + 1/x)^2 = 23 + 2 = 25.

Answer 2

Step-by-step explanation:

\begin{gathered} {(x - \frac{1}{x} )}^{2} = {x}^{2} + { (\frac{1}{x}) }^{2} - 2 \\ x - \frac{1}{x} = \sqrt{{x}^{2} + { (\frac{1}{x}) }^{2} - 2} \\ x - \frac{1}{x} = \sqrt{23 - 2} \\ x - \frac{1}{x} = \sqrt{21} \\ x - \frac{1}{x} = \sqrt {21}\: or \: - \sqrt {21}\end{gathered}