Application of Basic Inequality: Maximum Product
If a > 0, b > 0, and their sum a + b is a constant S, then ab attains its maximum value (S²)/(4) if and only if a = b. Formula: ab ≤ ((a + b)/(2) ight)² = (S²)…
Syllabus path: Sets and Inequalities › Basic Properties and Solutions of Inequalities › The AM-GM Inequality
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CSCA Mathematics Formula Reference
Formula and explanation
If a > 0, b > 0, and their sum a + b is a constant S, then ab attains its maximum value (S²)/(4) if and only if a = b. Formula: ab ≤ ((a + b)/(2) ight)² = (S²)/(4) Explanation: Using the basic inequality to find the maximum product of two positive numbers.
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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