Question

If x^2+1/x^2=27 find out the value of x+1/x and x-1/x

Answer 1

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

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