[tex]x + \frac{1}{x} = 2 \\ x {}^{2} + \frac{1}{ {x}^{2} } =? \\ \\( x + \frac{1}{x}) {}^{2} = x {}^{2} + 2x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = 4 \\ x {}^{2} + 2 + \frac{1}{x {}^{2} } = 4 \\ x {}^{2} + \frac{1}{x {}^{2} } = 4 - 2 = 2[/tex]
