Anonymous at Sat, 15 Feb 2025 00:15:17 UTC No. 16586183

First determine the continued fraction
[math]x = \frac{1}{9 + \frac{1}{2+\frac{1}{9+ \ldots}}}[/math]
which has to satisfy the equation
[math]x = \frac{1}{9+\frac{1}{2+x}} = \frac{2+x}{19+9x}[/math]
This results in the quadratic equation [math]9x^2 + 19x = 2 + x[/math] which has the solutions [math] x_{1,2} = -1 \pm \sqrt{\frac{11}{9}}[/math]. Obviously, we need the positive solution, so [math] x = -1 + \sqrt{\frac{11}{9}}[/math].
The full continued fraction therefore has the value
[math] \frac{1}{1 + x} = \frac{1}{1 -1 + \sqrt{\frac{11}{9}}} = \sqrt{\frac{9}{11}}[/math], and by squaring, I've officially done [math]9/11[/math].

Anonymous at Sat, 15 Feb 2025 00:18:09 UTC No. 16586184

>>16586141
Same user as >>16586183
Just wanted to add that I like the idea!

Anonymous at Sat, 15 Feb 2025 01:33:44 UTC No. 16586227

>>16586183
Thank you for solving it.
I thought, that maybe no one would want to solve it.

>and by squaring, I've officially done 9/11.
Oh now I feel a little bit bad.
Or that you were maybe hurt.

But then you wrote:
>>16586184
>I like the idea!

Anonymous at Sat, 15 Feb 2025 02:23:29 UTC No. 16586245

>>16586183
Gay, do it with straight edge and compass

Anonymous at Sat, 15 Feb 2025 06:18:51 UTC No. 16586367

>>16586141
>>16586183
samefag

OP at Sat, 15 Feb 2025 09:40:52 UTC No. 16586483

>>16586367
>samefag
nope
i didn't post the solution

plus i would never end a post that way

plus i haven't used MathJaX in any of my posts thus far