Basic Inequality (Two - Variable Form)

For any non - negative real numbers a and b, we have: (a + b)/(2) ≥ √(ab) Equality holds if and only if a = b. Explanation: This is a special case of the AM -…

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 a and b, we have: (a + b)/(2) ≥ √(ab) Equality holds if and only if a = b. Explanation: This is a special case of the AM - GM inequality when n = 2, and is the most commonly used form of the basic inequality.

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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