Uploaded February 2025 | Updated September 2026, 1 week ago

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I just learned this cubic formula with cosine from Wikipedia. The idea is to solve the depressed cubic equation x^3+px+q=0 with the triple angle identity of cosine. However, I don't think this formula is any useful. But is it cool? YES!

How to depress a general cubic polynomial ax^3+bx^2+cx+d youtu.be/ULsPhWmqhyc?si=GhAQTzUXV1vmu15P&t=545
The cos(3x) identity: youtu.be/ONKPlyN1hpo?si=rP3Ykm18YAnNho0l
Cubic Equations on Wikipedia: en.wikipedia.org/wiki/Cubic_equation

0:00 Solve x^3-28x+48=0
4:36 The proof
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