You will never forget how to solve quadratic equations once you see how Babylonians did it back in 2000 B.C. It’s striking that these methods date back 4000 years!
Quadratic equations are everywhere. You see some manifestation of it, often as parabolas, every single day. For example:
Babylonians, who lived in the fertile region between Euphrates River and Tigris River were also interested in quadratic equations. Consider this cute puzzle from 2000 B.C.
I have added the area and two-thirds of [ the side of ] my square and it is 35. What is the side of my square?Babylon puzzle from 2000 B.C.
In modern notation, this puzzle corresponds to solving for in
Babylonians had a geometric way of solving such equations. Let me explain. To solve a general quadratic equations of the form
Babylonians considered the following square.
The area of the larger square with side length is the sum of the areas of the individual squares and rectangles shaded in various colors above. Therefore,
Now, . This gives
Here is a trivia if you enjoyed reading this far.
Why did the Babylonians represent a general quadratic equation in the form , as opposed to the contemporary form ?
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