Application of Basic Inequality: Minimum Sum
If a > 0, b > 0, and their product ab is a constant P, then a + b attains its minimum value 2√(P) if and only if a = b. Formula: a + b ≥ 2√(ab) = 2√(P) Explana…
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
If a > 0, b > 0, and their product ab is a constant P, then a + b attains its minimum value 2√(P) if and only if a = b. Formula: a + b ≥ 2√(ab) = 2√(P) Explanation: Using the basic inequality to find the minimum sum 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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