Find the Value
\[ x – \frac{1}{x} = -1 \]
Find: \[ x^2 + \frac{1}{x^2} \]
Solution:
Using identity:
\[ \left(x-\frac{1}{x}\right)^2 = x^2 + \frac{1}{x^2} – 2 \]
\[ (-1)^2 = x^2 + \frac{1}{x^2} – 2 \]
\[ 1 = x^2 + \frac{1}{x^2} – 2 \]
\[ x^2 + \frac{1}{x^2} = 1 + 2 \]
\[ = 3 \]