Nice! A beautiful little kata demonstrating good technique and presentation. The one thing I might do differently is to reformat the final line with the half under the second factor, - so I could more readily make the trigonometric comparison as a lead-in to Fundamental Theorem of Algebra.
@@WartinLutherKing I'm not sure where you're going with that comment. There is a generalized cubic formula. It's not commonly emphasized in high school or college curricula, but it's definitely math. No doubt the reason most people don't know it is because it's significantly more complicated than the quadratic formula. There's also a generalized solution for quartic equations, and that one's complicated enough to fill a page. The history behind the development of the cubic formula and the proof that there is no generalized formula for finding the roots of quintic or higher degree polynomials are interesting bits of math history in their own right.
Why making so much mess? Just make the equation x³ = 3 (x/³√3)³ = 1 Now, the cube roots of unity are ω, ω² and 1. This means, x/³√3 = ω,ω²,1 This means, x = ³√3ω or ³√3ω² or ³√3 If you know about complex numbers, then you the value of cube roots of unity (omega ω).
Couldn't you have (more easily) just added 3 to both sides and then cube root both sides rather than all of that work? 😭 Or am I just missing the point of the video 😅
@@adrian_kayethey are still the "solutions" of the given equation and according to mathematical conventions you are supposed to include all solutions of an equation unless provided some condition. You will be incorrect if you mention only one root in any form of paper or dissertation
@@srinjansingharoy202 They have the same answer I’m just saying that this is the most visible and obvious solution with no extra steps, in this specific equation
@@adrian_kayeDifferent inputs can yield the same output, you need to list all inputs. All the inputs are mathematically not the same, even if they have the same output.
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Thanks for showing a different way of doing it, normally i would use 2nd moivre law to find the complex routes.
Nice! A beautiful little kata demonstrating good technique and presentation. The one thing I might do differently is to reformat the final line with the half under the second factor, - so I could more readily make the trigonometric comparison as a lead-in to Fundamental Theorem of Algebra.
Sigh. No one ever uses the cubic formula! j/k
Lol. I almost did. I will make a video someday.
Bro it's maths🤫🥶
@@WartinLutherKing I'm not sure where you're going with that comment. There is a generalized cubic formula. It's not commonly emphasized in high school or college curricula, but it's definitely math. No doubt the reason most people don't know it is because it's significantly more complicated than the quadratic formula. There's also a generalized solution for quartic equations, and that one's complicated enough to fill a page. The history behind the development of the cubic formula and the proof that there is no generalized formula for finding the roots of quintic or higher degree polynomials are interesting bits of math history in their own right.
@@PrimeNewtonspls what's the apps used
Yeah, and for a reason. 😄
Why making so much mess? Just make the equation
x³ = 3
(x/³√3)³ = 1
Now, the cube roots of unity are ω, ω² and 1.
This means,
x/³√3 = ω,ω²,1
This means,
x = ³√3ω or ³√3ω² or ³√3
If you know about complex numbers, then you the value of cube roots of unity (omega ω).
Indeed that's how we solve x^n = k... The solutions are k*exp(i(2rπ/n)) where r = 0,1,...,n-1.
Good
Absolutely. I just can't teach my algebra students that yet.
correct roots of unity, perfect
well, we did the same thing, just with showing what is omega
Just use nth unit root and adapt to -3 instead -1.
just take the 3rd root of 3, and then multiply by the 3rd roots of 1.
This question is very easy with highschool in Vietnam
I probably would have used De Moirve’s theorem
Great
Couldn't you have (more easily) just added 3 to both sides and then cube root both sides rather than all of that work? 😭 Or am I just missing the point of the video 😅
There are 3 solutions for a cubic equacion, you mencioned 1, he made the other 2
@meunomeeeu3118 ohhh okay
@@batimgamer126, no you are right, you can use De moivre's formula to have the other two answers
After you get that, get other answers using roots pf unity.
What app?
One of the few problemsI can solve on this channel
In the quadratic formula part, how did it go from "-4(3)^(2/3)" to "(1-4)"?
Taking common
Please, which app are you using?
Good notes
SMH lazy these people don’t even find the Taylor series or the cube root of 3 these days 😔
xcube equals 3
x equals cube root of 3
....
....
....
..
.
.
.
Cubert 3 is clearly a root. We could have skipped many steps with euclidean division
3 is not a root 😂
@@jigglyCroissant Omg I have no clue what I was on when I wrote this comment
Somebody please explain how he split that cubic eqn into quadratic
Just do a long division (polynomial division) of (x^3 - 3) by (x - r) where r is the real root and you'll see.
This technique SAVE the Humans from disgusting cubic equations!! 😮😮😮😮😮🥰🥰🥰🥰🥰🥰🥰🥰🥰🥰🥰
怎麼樣還是跑不了背公式，氣死。😂🎉❤
公式解還行啦 國中必備
OMG I DIDN'T KNOW ABT THIS! COOL
guys whats the name of the song. M looking for it
Believer by Imagine Dragons
Can you make a video about Carnado's Method?
Cardano* . I have one
❤❤❤❤
But, the cube root of 3 cubed is 3, and 3-3=0?
Those answers in vid are secret answers :)
ooo
cool vid but the music preference 👎👎👎
In such equations you already know x^3=3, so x=3root(3)
This is only 1 out of the 3 solutions
@@aythanraherisoanjato3056 All other solutions are basically the same, but with more steps
@@adrian_kayethey are still the "solutions" of the given equation and according to mathematical conventions you are supposed to include all solutions of an equation unless provided some condition. You will be incorrect if you mention only one root in any form of paper or dissertation
@@srinjansingharoy202 They have the same answer I’m just saying that this is the most visible and obvious solution with no extra steps, in this specific equation
@@adrian_kayeDifferent inputs can yield the same output, you need to list all inputs. All the inputs are mathematically not the same, even if they have the same output.
Me: ³/3 ×e^((2iπ/3)*0or1or2)
👍 Agreed
Absolutely annoying song.
Da frick yall doing x³-3=0 can be way ezier just do (^⅓) so x-3^⅓ than do (+3^⅓) youll get x=3^⅓ (^⅓ means cubed root but i couldnt write that down)
you only found one solution. the point of this is to find all solutions including complex