Question

Find the value of x:x squared+1/x squared=38

Answer 1

x = 3 ± 2√2

Step-by-step explanation:

${x}^{2} + \frac{1}{ {x}^{2} } = 38 \\ \\ {(x - \frac{1}{x})}^{2} + 2.x. \frac{1}{x} = 38 \\ \\ {(x + \frac{1}{ x } )}^{2} + 2 = 38 \\ \\ {(x + \frac{1}{x}) }^{2} = 36 \\ \\ x + \frac{1}{x} = 6 \\ \\ {x}^{2} + 1 = 6x \\ \\ {x}^{2} - 6x + 1 = 0 \\ \\ x = \frac{ - ( - 6) \pm \: \sqrt{ {( - 6)}^{2} - 4.1.1 }}{2.1} \\ \\ x = \frac{6 \pm \: \sqrt{36 - 4} }{2} \\ \\ x = \frac{6 \pm \: \sqrt{32} }{2} \\ \\ x = \frac{6 \pm 4 \sqrt{2} }{2} \\ \\ x = 3 \pm \: 2 \sqrt{2}$