Inequality of Arithmetic and Geometric Means
Inequality of Arithmetic and Geometric Means or AM-GM is one of the most powerful inequalities when dealing with positive real numbers.
Statement
Section titled “Statement”In general:
For any real positive numbers
:
The equality holds if and only if
For 2 numbers:
Section titled “For 2 numbers:”For any real positive numbers
The equality holds if and only if
For 3 numbers
Section titled “For 3 numbers”For any real positive numbers
The equality hold if and only if
For 2 numbers:
Hence, the statement is true for all real positive number x,y