Arithmetic-Geometric Mean Inequality (AM-GM)
For any non-negative real numbers a₁, a₂,..., aₙ, we have: (a₁ + a₂ + ... + aₙ)/(n) ≥ \sqrt[n]{a₁ a₂... aₙ} Equality holds if and only if a₁ = a₂ = ... = aₙ.
Syllabus path: Sets and Inequalities › Basic Properties and Solutions of Inequalities › The AM-GM Inequality
CSCA Exam Prep
This formula is aligned to the CSCA undergraduate admissions exam syllabus. Continue with the linked tutorial and topic practice.
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CSCA Mathematics Formula Reference
Formula and explanation
For any non-negative real numbers a₁, a₂,..., aₙ, we have: (a₁ + a₂ + ... + aₙ)/(n) ≥ \sqrt[n]{a₁ a₂... aₙ} Equality holds if and only if a₁ = a₂ = ... = aₙ. Explanation: The arithmetic mean is always greater than or equal to the geometric mean.
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 real num…
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