Question

if x+1/x^2=7 find x+1/x x-1/x​

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ \\ ( {x + \frac{1}{x} })^{2} - 2 = 7 \\ \\ ( {x + \frac{1}{x} })^{2} = 9 \\ \\ x + \frac{1}{x} = 3 \\ \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ ( {x - \frac{1}{x} })^{2} + 2 = 7 \\ \\ ( {x - \frac{1}{x} })^{2} = 5 \\ \\ x - \frac{1}{x} = \sqrt{5}$