Variant of the Basic Inequality: a² + b² ≥ 2ab
For any real numbers a and b, we have: a² + b² ≥ 2ab Equality holds if and only if a = b. Explanation: This is an equivalent form obtained by expanding (a - b)…
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 real numbers a and b, we have: a² + b² ≥ 2ab Equality holds if and only if a = b. Explanation: This is an equivalent form obtained by expanding (a - b)² ≥ 0, and it applies to all real 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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