Basic Inequality (Sum of Squares Inequality)
Formula: a² + b² ≥ 2ab Conditions: a, b ∈ ℝ. Explanation: For any real numbers, the sum of their squares is greater than or equal to twice their product.
Syllabus path: Sets and Inequalities › Basic Properties and Solutions of Inequalities › The AM-GM Inequality
CSCA Exam Prep
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CSCA Mathematics Formula Reference
Formula and explanation
Formula: a² + b² ≥ 2ab Conditions: a, b ∈ ℝ. Explanation: For any real numbers, the sum of their squares is greater than or equal to twice their product. Equality holds if and only if a = b. This is a corollary of the AM-GM 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 real num…
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