Question

$if \: x - \frac{1}{x} = 2 \: \\ \\ find \: {x}^{2} + \frac{1}{ {x}^{2} }$
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Answer 1

$x - \frac{1}{x} = 2 \\ squares \: on \: both \: sides \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 \times x \times \frac{1}{x} = 4 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 4 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 2$