Question

x=3+2√2 find x + 1/x

Answer 1

Step-by-step explanation:

$x = 3 + 2 \sqrt{2} \\ = \frac{x + 1}{x} \\ = \frac{3 + 2 \sqrt{2} + 1 }{3 + 2 \sqrt{2} } \\ = \frac{4 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \\ = \frac{4 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ = \frac{(4 + 2 \sqrt{2} )(3 - 2 \sqrt{2} }{(3)^{2} - ( {2 \sqrt{2} )}^{2} } \\ = \frac{12 - 8 \sqrt{2 } + 6 \sqrt{2} - 8}{9 - 8} \\ = \frac{4 - 2 \sqrt{2} }{1} \\ = 4 - 2 \sqrt{2}$