Arithmetic-Geometric Mean Inequality (AM-GM Inequality)
Chinese equivalent: 算术-几何平均不等式
Arithmetic-Geometric Mean Inequality (AM-GM Inequality) For non-negative real numbers, the arithmetic mean is greater than or equal to the geometric mean, i.e.…
Syllabus path: Sets and Inequalities › Basic Properties and Solutions of Inequalities › The AM-GM Inequality
CSCA Exam Prep
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CSCA Mathematics Exam Glossary
Definition
Arithmetic - Geometric Mean Inequality (AM - GM Inequality) For non - negative real numbers, the arithmetic mean is greater than or equal to the geometric mean, i.e., (a + b)/(2) ≥ √(ab).
Related tutorial and examples
The AM-GM Inequality
The AM - GM Inequality In the CSCA exam, the AM - GM Inequality (Arithmetic Mean - Geometric Mean) is the nuclear weapon for solving optimization problems (Max/Min), especially those involving reciprocal relationships (like x and (1)/(x) ). 1. Core Formula For any two positive re…
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