Question

if x + x^-1 = 11, evaluate x^2 + x^-2​

Answer 1

Step-by-step explanation:

$x + {x}^{ - 1} = 11 \\ = > x + \frac{1}{x} = 11 \\ \\ now \\ {x}^{2} + {x}^{ - 2} \\ = {x}^{2} + \frac{1}{ {x}^{2} } \\ = {(x + \frac{1}{x}) }^{2} - 2.x. \frac{1}{x} \\ = {11}^{2} - 2 \\ = 121 - 2 \\ = 119$