Find the Value
\[ x^2 + \frac{1}{x^2} = 79 \]
Find: \[ x + \frac{1}{x} \]
Solution:
Using identity:
\[ \left(x+\frac{1}{x}\right)^2 = x^2+\frac{1}{x^2}+2 \]
\[ \left(x+\frac{1}{x}\right)^2 = 79+2 \]
\[ \left(x+\frac{1}{x}\right)^2 = 81 \]
\[ x+\frac{1}{x} = \pm 9 \]