Difference between revisions of "User:Johnxyz1"
m |
m |
||
Line 6: | Line 6: | ||
<cmath>\begin{align*} | <cmath>\begin{align*} | ||
x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \ | x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \ | ||
− | &+ \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \ | + | & + \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \ |
− | &\text{(I copied it from another website but I typeset it myself; I am pretty sure those are not copyrightable. I still need \textit{years} to understand this.)} | + | &\text{(I copied it from another website but I typeset it myself;}\ |
+ | &\text{I am pretty sure those are not copyrightable. I still need \textit{years} to even understand this.)}\ | ||
+ | &\text{This is the cubic formula, although it is \textit{rarely} actually used and memorized a lot. The equation is}\ | ||
+ | &ax^3+bx^2+cx+d=0 | ||
\end{align*} | \end{align*} | ||
</cmath> | </cmath> | ||
+ | |||
+ | |||
+ | Source code: | ||
+ | |||
+ | https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm |
Revision as of 19:38, 21 June 2024
Below are some stuff I am doing to practice (that logo typeset by \LaTeX
looks a bit off). That does not mean I know all of it.
Source code:
https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm