Germany | Can you solve this ? | A Nice Math Olympiad Problem

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6 ай бұрын

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Пікірлер: 26

@AnimatiOFF14014 6 ай бұрын

Very good, let's watch the video!

@feelalive4374 6 ай бұрын

1 is the only correct answer.

@BartBuzz 6 ай бұрын

The only answer that can be calculated is "1". The complex solutions are extraneous.

@shmuelzehavi4940 6 ай бұрын

That's right. This video clip presented an operation consisting of a sum of 2 cubic roots of real numbers. The clip showed that the result must satisfy a cubic equation, but this does not imply that every one of the cubic roots is a result of the sum, which must be single valued (and real).

@krishnadeo7250 5 ай бұрын

Inspiring.

@daddykhalil909 6 ай бұрын

I am speechless A very good sequence of logical reasoning Thank you

@nagarajahshiremagalore226 3 ай бұрын

Well solved.

@cachotrelles4715 6 ай бұрын

Totalmente excelente 👌👌👏👏👏

@is7728 6 ай бұрын

Actually there are more complex roots. At 4:20, you simply consider the cube root of -1 as -1 and not for the other two complex roots.

@ManjulaMathew-wb3zn 6 ай бұрын

You are absolutely correct. If they want to consider complex solutions then complex values of ab shouldn’t be overlooked. The other option is to consider all real values only.

@ZoidVERSE 6 ай бұрын

wait what do you mean?

@is7728 6 ай бұрын

@@ZoidVERSE ab = 3√-1 (ab)^3 = -1 (ab)^3 + 1^3 = 0 (ab + 1) (a^2 * b^2 - ab + 1) = 0 So you get ab + 1 = 0 and (a^2 * b^2 - ab + 1) = 0 The answer from the linear root is -1 but there is still a quadratic root. After factorizing, you will get 2 more roots, which are complex.

@ZoidVERSE 6 ай бұрын

@@is7728 ahh I get it. thank you for explaining it

@samuelbenet007 5 ай бұрын

Seule la solution réelle est exacte !

@cachotrelles4715 6 ай бұрын

Excelente explicación en el idioma de las matemáticas. Muy buena la explicación del término + 3ab.x . Gracias

@prime423 6 ай бұрын

One root is one..Using synthetic division makes the solution obvious.In doing these problems, cogent observations save a lot oif work.

@user-uy3or9ii4n 6 ай бұрын

literally today I was interested in Cardano’s theorem for solving an equation of degree 3 and for myself I composed the equation x³+3x-4=0 The discriminant turned out to be D= q²/4+p³/27=4+1=5 hence x= (2+√5)^(1/3) +(2-√5)^(1/3) I tried for a very long time to bring this to 1, but I couldn’t do it myself! Thank you for the video. (compiled with the help of a translator, I apologize for any inaccuracies)

@ivansudakov6877 6 ай бұрын

Из чего следует, что i - вещественное число. И даже более того, i - это сразу два разных вещественных числа. 🤓 Используя полученные результаты, также можно легко доказать, что i = 0 и что 0 = 1.