Students will see several proofs of the AM-GM inequality. First, students will see three visual proofs.
Here's the first proof:
For the other two proofs, watch these videos by Micro Visual Proofs:
Next, students will see an algebraic proof.
AM/GM Inequality (2 of 2: Algebraic Proof) by Eddie Woo
Conclude by giving your students these challenges:
- Making a Difference by NRICH
- Gaxinta by NRICH
- 2008 AMC 8, Problem 15
- 2005 AMC 8, Problem 20
Remainders by NRICH: For the first two problems, replace "I'm thinking of a number," with "I'm thinking of a positive number." Do not give your students the challenging extension.