A common, and versatile inequality.

1𝑛∑𝑛𝑖=1𝑥𝑖=𝑛√𝑥1𝑥2⋯𝑥𝑛

Trivial extension:

1𝛼∑𝛼𝑖𝑥𝑖=𝛼√∏𝑥𝑎𝑖𝑖

Where 𝛼=∑𝛼𝑖.

Cauchy-Schwarz inequality

Applications

minimum sum of distances to asymptotes minimum distance from point to improper rational function

References