Question

if x^2 +1/x^2=27 find the values of each of the following:
x+1/x
x-1/x​

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 27 \\ ( {x + \frac{1}{x} })^{2} - 2 = 27 \\ ( {x + \frac{1}{x} })^{2} = 29 \\ x + \frac{1}{x} = \sqrt{29} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 27 \\ (x - \frac{1}{x} ) ^{2} + 2 = 27\\( x - \frac{1}{x}) ^{2} = 25 \\ x - \frac{1}{x} = 5$