Question

give me the solution and get 100 point free
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Answer 1

$given \: \: \: \: x + \frac{1}{x} = \sqrt{5} \\ squaring \: both \: sides \\ ( {x + \frac{1}{x} })^{2} = 5 \\ (x - \frac{1}{x} ) ^{2} + 4 =5 \\ ( {x - \frac{1}{x} })^{2} = 1 \\ x - \frac{1}{x} =± 1 \\ finding \: \: \: \: {x}^{2} - \frac{1}{ {x}^{2} } = (x - \frac{1}{x} )(x + \frac{1}{x} ) \\ = 1 \times \sqrt{5} \: \: \: \: (if \: \: \: x - \frac{1}{x} = 1)\\ = \sqrt{5} \\ or \\ {x}^{2} - \frac{1}{ {x}^{2} } = ( - 1) \times \sqrt{5} \\ = - \sqrt{5} \: \: \: \: (if \: \: \: x - \frac{1}{x} = - 1)$

Answer 2

Answer:

I don't appreciate your dis-honest behaviour. We only get 50 points but you told 100.