Solution to AM - GM Introductory Problem 1
For nonnegative real numbers , demonstrate that if then .
Since , the geometric mean () must also equal .
The AM-GM Inequality states that the arithmetic mean of a set of non-negative numbers is greater than or equal to the geometric mean, so that means that .
Rearranging, we get , as required.
Back to the Arithmetic Mean-Geometric Mean Inequality.