Question

Please help me in the below attached question

Answer 1

${x}^{2} - 2x - 1 = 0$

Divide whole equation by x, we get

${x} - 2 - \frac{1}{x} = 0$

${x} - \frac{1}{x} = 2$

Squaring both sides,

${(x - \frac{1}{x}) }^{2} = {2}^{2}$

${x}^{2} - (2 \times x \times \frac{ - 1}{x} ) + \frac{1}{ {x}^{2} } = 4$

${x}^{2} + 2 + \frac{1}{ {x}^{2} } = 4$

${x}^{2} + \frac{1}{ {x}^{2} } = 4 - 2$

${x}^{2} + \frac{1}{ {x}^{2} } = 2$