Students will learn how to solve quadratics using u-substitution. Here's a lesson, and here's practice.
Conclude by giving your students these challenges:
- This Fencing by NRICH
- Rectangle Tangle by NRICH
- 2005 AMC 8, Problem 4
- 2017 AMC 8, Problem 4
Near the end of The Wizard of Oz, the Scarecrow says "the sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side." This exact statement is also reiterated by Homer Simpson, in season 5, episode 19 of The Simpsons. Prove or disprove it. After doing so, prove or disprove its generalization for any triangle, isosceles or not. That is, if \(a,\) \(b,\) and \(c\) are sides of a triangle, prove or disprove that \(\sqrt{a} + \sqrt{b} = \sqrt{c}.\) Here are both solutions.