cppio · May 12, 2020 02:10
diff --git a/cubic.tex b/cubic.tex
 \[
 x=\sqrt[3]{-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}+\sqrt{\left(-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}+\sqrt[3]{-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}-\sqrt{\left(-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}-\frac{b}{3a}
 \]
diff --git a/cubic2.tex b/cubic2.tex
 \[
 \newcommand{\p}{-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}}
 \newcommand{\q}{\sqrt{\left(\p\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}
 x=\sqrt[3]{\p+\q}+\sqrt[3]{\p-\q}-\frac{b}{3a}
 \]
	\[
	x=\sqrt[3]{-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}+\sqrt{\left(-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}+\sqrt[3]{-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}-\sqrt{\left(-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}-\frac{b}{3a}
	\]
	\[
	\newcommand{\p}{-\frac{b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}}
	\newcommand{\q}{\sqrt{\left(\p\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}
	x=\sqrt[3]{\p+\q}+\sqrt[3]{\p-\q}-\frac{b}{3a}
	\]