Find the Value
\[ x^2 + \frac{1}{x^2} = 66 \]
Find: \[ x – \frac{1}{x} \]
Solution:
Using identity:
\[ \left(x-\frac{1}{x}\right)^2 = x^2+\frac{1}{x^2}-2 \]
\[ \left(x-\frac{1}{x}\right)^2 = 66-2 \]
\[ \left(x-\frac{1}{x}\right)^2 = 64 \]
\[ x-\frac{1}{x} = \pm 8 \]