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

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