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The AM-GM Inequality

Discover why the average of two numbers is never less than their geometric mean and use it to solve optimization problems.

Grade 12Math OlympiadMathLogicGeometryNumber SenseAdvanced1 to 1.7 hr3 materials

What you'll learn

  • State and prove (a + b) divided by 2 is at least the square root of ab
  • Know when equality holds
  • Apply AM-GM to optimization problems

Objective

Prove the AM-GM inequality for two numbers, test it with data, and apply it to find maximum and minimum values.

STEM concepts

InequalitiesProofOptimizationEquality conditions
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Step-by-step instructions
Prediction, test sheet and results
Why does it work, challenge and project report

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