Given that
[tex]x + \frac{1}{x} = 9[/tex]
[Square both sides]
[tex](x + \frac{1}{x})^2 = 9^2[/tex]
The Algebraic Formula:
[tex](a+b)^2 = a^2 + 2(a)(b) + b^2[/tex]
Therefore:
[tex]x^2 + 2(x)(\frac{1}{x}) + ( \frac{1}{x})^2 = 9^2[/tex]
[Evaluate the terms]
[tex]x^2 + 2+ \frac{1}{x^2} = 81[/tex]
[-2 on both sides]
[tex]x^2 + \frac{1}{x^2} = 81 -2 [/tex]
[Evaluate the right side]
[tex]x^2 + \frac{1}{x^2} = 79[/tex] (Answer B)
