Example Application
Consider the function
for all positive real numbers x, y and z. Suppose we wish to find the minimal value of this function. First we rewrite it a bit:
with
Applying the AM–GM inequality for n = 6, we get
Further, we know that the two sides are equal exactly when all the terms of the mean are equal:
All the points (x,y,z) satisfying these conditions lie on a half-line starting at the origin and are given by
Read more about this topic: Inequality Of Arithmetic And Geometric Means
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