Find the Value
\[ x + \frac{1}{x} = 11 \]
Find: \[ x^2 + \frac{1}{x^2} \]
Solution:
Using identity:
\[ \left(x+\frac{1}{x}\right)^2 = x^2 + \frac{1}{x^2} + 2 \]
\[ (11)^2 = x^2 + \frac{1}{x^2} + 2 \]
\[ 121 = x^2 + \frac{1}{x^2} + 2 \]
\[ x^2 + \frac{1}{x^2} = 121 – 2 \]
\[ = 119 \]