SMO 2022 Open Q8: Maximizing 𝑥² + 𝑦² with a given constraint скачать в хорошем качестве

SMO 2022 Open Q8: Maximizing 𝑥² + 𝑦² with a given constraint

In this video, we explore a difficult math problem from the SMO Open 2022 competition. The problem involves finding the maximum possible value of 𝑥^2 + 𝑦^2 given the constraint (𝑥−2)^2 + (𝑦−3)^2 = 4, where 𝑥 and 𝑦 are real numbers. We discuss how to approach the problem step-by-step, including identifying the constraint as an equation of a circle, finding the center and radius of the circle, and using geometric intuition to determine the optimal values of 𝑥 and 𝑦. With resilient and persistent effort, we tackle the problem and arrive at the solution. Additionally, we explore a related question: what is the floor of (𝑆−17)^2, where 𝑆 is the largest possible value of 𝑥^2 + 𝑦^2? Through this problem, we demonstrate the value of perseverance and critical thinking in problem-solving. Join us for an educational and compelling journey into this intriguing math problem!