A common, and versatile inequality.

1𝑛𝑛𝑖=1𝑥𝑖=𝑛𝑥1𝑥2𝑥𝑛

Trivial extension:

1𝛼𝛼𝑖𝑥𝑖=𝛼𝑥𝑎𝑖𝑖

Where 𝛼=𝛼𝑖.

Cauchy-Schwarz Inequality

Applications

Minimum sum of distance to asymptotes

References