🗑️ 🧵 Untitled Thread
Anonymous at Mon, 1 Apr 2024 04:20:20 UTC No. 16107325
Let [math]P(x)[/math] be a polynomial with solution [math]\sqrt[3]{a} +\sqrt[3]{b}[/math] and [math]a,b \in Z[/math].
The general solution is [math]x^9-3(a+b)x^6-[/math] [-------------] [math]x^3-(a+b)^3[/math].
Fill in the missing part.
Anonymous at Mon, 1 Apr 2024 04:46:59 UTC No. 16107352
homework thread
Anonymous at Mon, 1 Apr 2024 04:50:21 UTC No. 16107355
>>16107352
Nah, I made this up. It’s too retarded to be homework.
Anonymous at Mon, 1 Apr 2024 06:32:37 UTC No. 16107460
>>16107325
[math]3(a^2-7ba+b^2)x^3[/math]
Anonymous at Mon, 1 Apr 2024 06:40:48 UTC No. 16107465
You have just landed in the rabbit hole of Sylvester Matrices, Resultants, and weird algebraic number tricks.
Anonymous at Mon, 1 Apr 2024 16:22:34 UTC No. 16107922
Also got [math]P(x) = x^9 - 3(a+b)x^6 + 3(a^2-7ab+b^2)x^3 - (a+b)^3[/math].
I just multiplied out [math]\prod_{m=0}^2 \prod_{n=0}^2 (x - \omega^m A - \omega^n B)[/math] where [math]\omega = e^{2\pi i/3}[/math].
Tedious but simple.
Anonymous at Mon, 1 Apr 2024 16:24:51 UTC No. 16107924
>>16107922
And where [math]A = \sqrt[3]{a}[/math], [math]B = \sqrt[3]{b}[/math].