Difference between revisions of "User:Johnxyz1"
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| + | Favorite topic: <cmath>\text{Counting \& Probability}</cmath> | ||
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| + | Favorite color: <cmath>\text{\textcolor{green}{Green}}</cmath> | ||
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| + | Favorite software: Excel | ||
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Below are some stuff I am doing to practice <math>\LaTeX</math> (that logo typeset by <code>\LaTeX</code> looks a bit off). That does not mean I know all of it. | Below are some stuff I am doing to practice <math>\LaTeX</math> (that logo typeset by <code>\LaTeX</code> looks a bit off). That does not mean I know all of it. | ||
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<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> | ||
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| + | Source code: | ||
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| + | https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm | ||
Revision as of 20:44, 21 June 2024
Favorite topic: ![\[\text{Counting \& Probability}\]](http://latex.artofproblemsolving.com/b/c/c/bcc448ef67345b970329c6e4921492fb5e4261cc.png)
Favorite color: ![\[\text{\textcolor{green}{Green}}\]](http://latex.artofproblemsolving.com/6/c/8/6c8a353f688e76bb1ed7de3f8a0640984e6070c1.png)
Favorite software: Excel
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.
![\[\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]](http://latex.artofproblemsolving.com/7/c/b/7cbf48dbdce18ee42c347668a9314410de651207.png)
![\[e^{i\pi}+1=0\]](http://latex.artofproblemsolving.com/2/6/c/26cc6b1c790a7db2144e4f5948158479292c55e6.png)
![\[\sum_{x=1}^{\infty} \frac{1}{x}=2\]](http://latex.artofproblemsolving.com/e/e/5/ee5784ec0e67d8ddb8d721443e25e5a727e1cf76.png)
![\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}} \\ & + \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;}\\ &\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*}](http://latex.artofproblemsolving.com/f/0/8/f08f932bc16a96f0869fb3aafcfc578fde10bda5.png)
Source code:
https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm
