Question

x+1/x=3,xE R* calculati x^2+ 1/x^2

Answer 1

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