Math Olympiad: Solving for a + b + c in an Algebra Problem

A beautiful algebra problem from the Math Olympiad: Given ab = 40, bc = 50, ca = 60. Find the value of a+b+c. This problem is a fantastic test of your skills in solving systems of equations and manipulating radicals. In this video, I'll walk you through a clear, step-by-step solution that reveals an elegant answer. We solve it without a calculator, using pure algebraic techniques perfect for math competitions. Solution Walkthrough: 0:00 Introducing and setting Up the System of Equations 0:15 The Key Trick (Multiplying All Equations) 1:30 Simplifying the Square Root (Detailed Breakdown) 2:20 Solving for Each Variable (a, b, c) 5:50 The Final Sum - An Elegant Answer #mathtutorials #algebra #systemofequations #matholympiad #olympiadmathematics #radicalsimplification #squareroots #howtosolvesystems #mathproblemsolving #stepbystepalgebra #nicealgebraproblem #mathchallenges #mathpuzzles #mathtricks Explore more at Mathitect. 👉 Subscribe for more tutorials: https://www.youtube.com/@Mathitect/ 👉 Instagram: https://www.instagram.com/mathitect 👉 Facebook: https://www.facebook.com/mathitect 👉 Tiktok: https://www.tiktok.com/@mathitect