Скачать или смотреть Finding a+b+c from ab, bc, and ca: An Algebraic Insight

Is it possible to find the sum of three unknown numbers if you only know the products of each pair? This video explores that exact puzzle: given that ab = 120, bc = 180, and ca = 240, we will determine the value of a + b + c.

The solution involves a clever manipulation that reveals the relationship between the given products and the desired sum, demonstrating a beautiful piece of algebraic reasoning.

In this video, we'll walk through:

The key insight of multiplying all three given equations together.
How this multiplication leads to the value of (abc)².
The step of taking the square root to find the product abc.
How to use abc to finally deduce the sum a + b + c.

A satisfying solve that highlights an elegant and non-obvious algebraic technique.

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