For this case we have the following number:
[tex]x = 3 + 2 \sqrt{2} [/tex]
We have the following expression:
[tex]x + \frac{1}{x} [/tex]
Substituting values and rewriting we have:
[tex]1 + \frac{1}{3 + 2 \sqrt{2}}
\frac{(3 + 2 \sqrt{2})^2 + 1}{3 + 2 \sqrt{2}}
\frac{3^2 + 24\sqrt{2} + 8}{3 + 2 \sqrt{2}}
\frac{9 + 24\sqrt{2} + 8 }{3 + 2 \sqrt{2}}
\frac{17 + 24\sqrt{2}}{3 + 2 \sqrt{2}}
[/tex]
Answer:
The nature of the number x + 1 / x will be:
[tex]\frac{17 + 24\sqrt{2}}{3 + 2 \sqrt{2}}
[/tex]
