Question

if x=3+2√2 check whether x+1\x is a rational or irrational

Answer 1

it is an irrational number

Answer 2

$x = 3 + 2 \sqrt{2} \\ theref ore\ \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \\ = \frac{1(3 - 2 \sqrt{2}) }{(3 + 2 \sqrt{2} )(3 - 2 \sqrt{2} )} \\ = \frac{3 - 2 \sqrt{2} }{9 - 8} = 3 - 2 \sqrt{2} \\ \\ \\ x + \frac{1}{x} = 3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} = 6$
so it is a rational number