Basic Inequality (Arithmetic - Geometric Mean Inequality)
Formula: (a + b)/(2) ≥ √(ab) Conditions: a ≥ 0, b ≥ 0. Explanation: The arithmetic mean of two non - negative real numbers is greater than or equal to their ge…
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
Formula: (a + b)/(2) ≥ √(ab) Conditions: a ≥ 0, b ≥ 0. Explanation: The arithmetic mean of two non - negative real numbers is greater than or equal to their geometric mean. Equality holds if and only if a = b.
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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