\documentclass[11pt]{scrartcl}
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\begin{document}
\title{H3278100}
\subtitle{Evan Chen}
\author{Twitch Solves ISL}
\date{Episode 140}
\maketitle

\section*{Problem}
Let $a$, $b$, $c$ be positive real numbers such that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1$.
Show that
\[ a+b+c \leq \sqrt{b^3+ac^2+a^2c}. \]

\section*{Video}
\href{https://www.youtube.com/watch?v=sJsAqXuGj-A&list=PLi6h8GM1FA6yHh4gDk_ZYezmncU1EJUmZ}{\texttt{https://youtu.be/sJsAqXuGj-A}}

\section*{External Link}
\url{https://aops.com/community/p30181272}

\newpage

\section*{Solution}
Note that by Cauchy-Schwarz the inequality
\[ \left( b^3 + a^2c + ac^2 \right)
    \left( \frac 1b + \frac 1c + \frac 1a \right)
    \ge (b+a+c)^2 \]
holds for all $a,b,c > 0$ which is what we wanted.

\end{document}
