There are two real solutions. Substitute x=n^3 and you get the quadratic x^2 -x = 2. Then you will find that n = -1 and n= 2^(1/3)

@onlineMathsTV

11 ай бұрын

Very very correct @Tony Martinez. You are good at it sir. Much respect and love to you boss...👍👍💖💖

@abdulhameedyekeen3245

11 ай бұрын

Exactly

@belhimoncef1

10 ай бұрын

❤

@user-sk8zo8gj4z

10 ай бұрын

&G?{❤😊😂 8

@Patricotification

10 ай бұрын

Yes, I find the same results as you by changing the variable X = x3

I am 66 but love maths and didn’t love it enough in high school! Thanks.

Задачка тянет максимум на уровень проверочной работы восьмого класса

n^6-n^3=2 -2 from both sides let x=n^3 x^2-x-2=0 (one quadratic formula later) x=2 x=-1 x=n^3 => n=cbrt(-1)=-1 n=cbrt2 edit: ima try to find the imaginary roots just for fun x^6-x^3-2=0, if y=x^3, y^2-y-2=0 to factor y^2-y-2, 2 numbers (a & b) must satisfy a+b=-1 & ab=-2 =>a=-2 & b=1 => y^2-y-2=(y-2)(y+1) y=x^3, => x^6-x^3-2=(x^3-2)(x^3+1) x^3-2=0 x1=cbrt2, so we can do (x^3-2)/(x-cbrt2)= x^2+xcbrt2+cbrt4 to find the others. [1 quadratic formula later] x=+/-sqrt(-cbrt2-cbrt4) =+/-(isqrt(cbrt2+cbrt4)) x^3+1=0 x1=-1, do the same thing, (x^3+1)/(x+1)=x^2-x+1 [1 quadratic formula later] x=(1+/-isqrt3)/2 x1=cbrt2 x2=isqrt(cbrt2+cbrt4) x3=-isqrt(cbrt2+cbrt4) x4=-1 x5=(isqrt3+1)/2 x6=(1-isqrt3)/2

@onlineMathsTV

11 ай бұрын

You the best sir....😍😍😍

Excellent. But in Japan , Highschool students solve this question with complex plane. if n^3=2 , they think that n = r(cos𝜽 + isin𝜽) then other solution are 2^1/3(cos2/3𝛑+isin2/3𝛑) and 2^1/3(cos4/3𝛑+isin4/3𝛑), I think.All solution in this case exist 6 pattern.

√-3=√-1×√3の式変形について、今回は良かったけど基本的にはa.b>0の条件付きで√a×√b=√abが成り立つので、数学的には良くないことをしてる事を自覚してから動画出していただきたい。

It's could be easier to do this with quadratic function and delta but this answer is also good

Thanks for the tips to determine if a quadratic function will give real roots or not

@onlineMathsTV

Жыл бұрын

You welcome always...much love 💖💖💖

It' s much simpler (just a couple of passages...) using Ruffini' s rule, once you recognize that n = -1 is one of the roots. The other real solution is cubic root of 2 (2^(1/3))

@onlineMathsTV

11 ай бұрын

Bravo....👍👍👍

решается в уме. пусть n^3=a. т.е. у нас а^2-а=2 а(а-1)=2*1 следовательно а=2 n^3=2 n=2^(1/3) При а=-1 n =-1

@onlineMathsTV

11 ай бұрын

Bravo👍👍👍

Valeu professor!!!

More interesting to cover all 6 solutions, and their intertwined relationship with the complex roots w where w^3 = +1

Great job, professor!

Well explained. God bless you too.

Nice job, as usual.

Thank you for reminding us that there are, in general, six solutions to a 6th order equation. It would be more challenging to ask for all of the distinct solutions. Excellent video!.

@88kgs

6 ай бұрын

100% agree

Great explanation 👌

We can get six solutions .i give you three. n= -1 or n=(2)^1/3 or n=(i)^2/3 ..... Thank you bro.

great teacher

Parabéns irmão. Ótimo trabalho!

تمرين جميل جيد . شرح واضح مرتب . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم جميعا. تحياتنا لكم من غزة فلسطين .

@jakeswealthworld1039

Жыл бұрын

Wonderful

@onlineMathsTV

Жыл бұрын

Wow!!! what a wonderful prayer from a wonderful human/fellow from Gaza, Palestine. A loudest amen I and my team say to your awesome prayers sir. All of us @onlinemathstv love you and we also pray the Almighty God to protect and shine His face on you and your entire family members. Hope to meet with you one-on-one some days to come. We love you sir....💖💖💕💕❤️❤️😍😍

Excelente aula !

@onlineMathsTV

10 ай бұрын

Thanks for appreciating our little effort sir. Also thanks for watching and dropping this wonderful words of encouragement.

excellent video

Thank you. a better and shorter solution is (N^3) (N^3 - 1) = 2 and since 2 = 1x 2, then (N^3 - 1) = 1 and N^3 = 2

@WhiteGandalfs

3 ай бұрын

Yes, but only applicable in case of request of integer solutions. In the case of request of "real" values, prime decomposition is irrelevant.

step 2:45 to 4:00 normally done in one go. thanks for the vid

Thanks

@onlineMathsTV

Жыл бұрын

You are most welcome sir. One love from all of us @onlinemathstv.

Excellent Sir

Very beautiful

good exercise thank you

@onlineMathsTV

11 ай бұрын

You are most welcome sir. We are glad you gained some values from our video. Much love sir...💖💖💕💕

Excelent video.

@onlineMathsTV

7 ай бұрын

Thanks for watching and leaving behind this wonderful comment sir. We love you....💕💕💕😍😍😍

Nice

@onlineMathsTV

Жыл бұрын

Thanks sir...❤️❤️

Можно через замену n^3=t, t^2-t-2=0, t=-1,t=2, n= -1, n= корень кубический 2.

@ontixor2821

8 ай бұрын

Да! Это очень простая задача. Если это реально есть в чьей-то олимпиаде, то мне жаль их систему образования.

very good my friend

P2-P-2=0 we use quadratic trinomial decomposition A x B = -2 and A+B = -1 .......(P-2)(P+1)....in order for these 2 numbers to "come out", both are negative, one term must be + and the other minus, and since it is a simple quadratic equation, there must be 1 and 2😉 -2x1=-2 and -2+1=-1 this way is usually faster

@onlineMathsTV

11 ай бұрын

Great approach boss. Lovely sir. You the best because you are good at what you know. Respect sir...👍👍👍

Reasonless effort 🌈🌈🌈Rainbows

clearly communicated and easy to follow, great work!

@onlineMathsTV

11 ай бұрын

Glad it was helpful! Thanks for dropping a comment to encourage us sir. Much love💕💕💕

@user-sk8zo8gj4z

8 ай бұрын

"8*T>`&q)L )5Ps\ U wpQ"aP

Literally,You are legend 😮😮❤❤❤ keep it up

GENIAL!!!

🇮🇶🇮🇶🇮🇶Good explanation. The topic of mathematical foundations requires multiple skills and ideas. From Iraq

@onlineMathsTV

10 ай бұрын

Smiles...thanks for the compliments and thanks for watching our contents. Much love from Onlinemathstv 💕💕❤️❤️💖💖

Muy bien hermano.

@onlineMathsTV

7 ай бұрын

Thanks a million my dear. Much love 💖💖💕💕😍

Una maniera assurda per complicare un calcolo semplicissimo che si può fare a mente... Ridicolo!

数学って素晴らしいな 喋る言語は違うけど、繋がれる。

nice job

@onlineMathsTV

10 ай бұрын

thanks for the appreciation

If you taking an exam with time limit you wont make it. You already have n^3=2 take the cuberoot of 2 which is 2^1/3 thats the final answer substitute it to the original equation n^6-n^2=2 and your done no need to go to difference of two cube equation GOT IT!!!

@onlineMathsTV

10 ай бұрын

Got it master. Thanks for this approach, you the boss here. Respect 🙏🙏🙏

Nice math

@onlineMathsTV

11 ай бұрын

Thanks sir. We love you for watching and comment sir.....💖💖💖

Voce explica muito bem Deixa a matemática fácil 😘

@onlineMathsTV

10 ай бұрын

Smiles, thanks for this wonderful encouraging words of urs.

@janetedossantoscardoso8444

10 ай бұрын

@@onlineMathsTV 🙏

solved within 5 mins, and that's because I have not touched any math question for over a decade, that's junior highschool grade math, all you need to know is (a+b)^2 = a^2 + 2ab+ b^2,

@St0n3dCold

6 ай бұрын

Was thinking the same, this is not even close to be an "olympiad question"

Great job friend🎉 I am Indian

My solution: N^6 = (N³)² Trick - N³ = X 1) X² -X -2 = zero By baskara, X' = 2 ; X" = -1 Then , N³ = 2 N = 1,25999 ( bY using my cell calculator ) Saludo from Brazil!!!

Really, this was a question in IMO? The questions I got in INMO( Indian National Mathematics Olympiad) were much harder than this.

This is solved in the mind

@onlineMathsTV

10 ай бұрын

sure

so cool :) have a nice day!

@onlineMathsTV

6 ай бұрын

Thanks a million sir. You have a wonderful and a lovely day sir. Much respect my friend...🙏🙏🙏👍👍👍👍.

Great👍. Sir we can also do it by hit and trial method, that is by assuming n=0, 1, -1, 2, -2..... We can get the answer quickly 🙏. Regards

@onlineMathsTV

11 ай бұрын

Very very correct sir. Respect.....👍👍👍

@josemaholo8651

11 ай бұрын

Too long procedure for nothing...

@88kgs

6 ай бұрын

​@@onlineMathsTV, Sir today when I saw your this video again, after 5 months, i realised that you explained it so very well in detail.. When we have to find all the values including the imaginary once.. your way is the best.. Thank you so much Sir.. Regards 🙏🙏

@88kgs

6 ай бұрын

​@@josemaholo8651, we are taught this way for solving such problems mentally and checking the answers, before solving it.. this makes the approach easy and confident.. 😊🙏

👍👍👍

@onlineMathsTV

Жыл бұрын

Thanks for the encouragement sir. We love you for watching and at the same time commenting.

Thanks for a job well done Jakes

@onlineMathsTV

Жыл бұрын

You are welcome all the time ma

@hogec_enlightenmentarena6975

Жыл бұрын

Great job at that

Which phone are you using to do this pls? And light system?

n=exp(i*Pi) j'ai trouvé en 10 secondes ...

2 reality and 4 complexity

Base on my algebra knowledge you can not do 2 unknown value cause i have examples too x + x = 10 5+5 is 10, 6+4 is also 10, 7+3 is also 10 but it is impossible to pick in this 3 solution because they are two unknown value

Very long slution but good

n=-1 , n= ³√2

at least you can point out there are 6 roots!

Math Paralympic?

even exponent makes negative number positive odd exponent makes negative number negative its definitely and clearly not 2 because 2^n is very famous (binary numbers) Solve these problems without algebra. Use theories, theorems, and common sense if you plug in values like 2 its clearly not 2 so it must be under 2 try -1 and 1 1 gives it 0 -1 gives it 2

lmao this is so easy, i did in like 20 seconds, i dont think it would be something that pops up on the IMO 😂

@St0n3dCold

6 ай бұрын

yeah fr the title is clickbait

once you get to P=n^3 = 2, you can go straight to n=2^1/3, you don't need to do all that other crap. Cube roots of real numbers are evenly spaced 120 degrees apart on a circle in the complex plane, with radius = real cube root. but there's only 1 real root in the X axis.

Hello sir. Once we get to n^3= 2 or n^3= -1 (5 min into the video), isn't the problem already almost solved? I mean, raise both equations to the power of (1/3) and you get, right away, the solutions, namely n= 2^(1/3) and n = (-1)^(1/3) = -1, and it's done. These are the only 2 real solutions of the initial equation; I mean, n^3 is a continuous function whose derivative is always positive (other than for n=0) and so there is only one solution for each n^3, whatever n^3 is. Of course we may try to work out the other solutions (which is what you did), but we already know that the other solutions won't be real but rather imaginary solutions.

@onlineMathsTV

10 ай бұрын

You are very correct sir. The further work is just to prove that the other solutions are imaginary. Thanks for watching our content and dropping this wonderful observation sir. Much love from all of us @onlinemathsTV ❤️❤️💖💖💕💕💕

Nhin chung các bài toan kiểu này quá dễ

Raíz cúbica de 2 también es valor de n

@onlineMathsTV

7 ай бұрын

Yes, you are very correct sir.

2^1/3

n^6-n^3-2=0 n^3=(1+-sqrt(1+8))/2=1+-3=4 or -2 n=cbrt(4) or cbrt(-2) RRT would have you believe there are 6 roots, so I’ll do it the cubic way: n^3(n^3-1)=2 n^3(n-1)(n^2+n+1)=2 I guess this would find them but i don’t see how to get rid of the 2.

@maxvangulik1988

9 ай бұрын

Just spotted n=-1 as a solution

Al ojo: raíz cúbica de 2

Đúng là giải toán kiểu tây. Dài dòng. Học sinh VN giải trong phút mốt.

@onlineMathsTV

11 ай бұрын

Wow, nice and great brains.

3rd root of 2

It’s -1, right? (-1) to the even power is 1, and (-1) to the odd power is -1, so 1 - (-1), or 1 + 1 = 2.

This is the easiest IMO question I’ve ever seen in my life

for me the Answers are cube root of 2 and -1

By International math Olympiad, does it mean IMO? Cuz i thought IMO questions would be very hard but this was taught in my school and i am not particularly good at math anways.

-1 or 2^(1/3)

Use log n^6 - n^3 = 2 log n^6 - log n^3 = log 2 6 log n - 3 log n = log 2 3 log n = log 2 log n = 1/3 log 2 log n = log 2^1/3 n = 2^1/3

p1+p2=1. p1×p2=-2. p1=2. p2=-1

i found six rooths n = {-1 , (1+isqrt(3))/2 , (1-isqrt(3))/2 , cbrt(2) , -cbrt(2) +- isqrt(3cbrt(2)) }

@onlineMathsTV

Жыл бұрын

👍👍👍 you the guru @Lucien34.

@lucien346

11 ай бұрын

@@onlineMathsTV guru ?

@boakyeprince8116

11 ай бұрын

Well depth in the subject matter… sorry for the jargon

tambem podia se "raiz cúbica de 2".

Bro you can just use cube root directly

2rac1/3 -1

good lesson but bad audio

1--1=2 n= -1

2^n-1 equal

Why did I get results different than yours (root #1: n = ³√2 and root #2: n = -1)? See below: Question: n⁶ - n³ = 2 n = ? Answer: n⁶ - n³ = 2 if N = n³ then n⁶ - n³ = 2 = N² - N = 2 N² - N - 2 = 0 delta = (-1)² - 4*1*-2 = 1 - (-8) = 9 √delta = √9 = 3 root #1: N = (-(-1) + 3)/2*1 = 4/2 = 2 N = n³ = 2 => n = ³√2 root #2: N = (-(-1) - 3)/2*1 = -2/2 = -1 N = n³ = -1 => n = ³√(-1) = -1 Result(s): n = ³√2 n = -1 🙂

@onlineMathsTV

11 ай бұрын

I will go through mine and urs and get back to you sir. Just give me some time.....

@oley7264

10 ай бұрын

Вы получили на 100% идентичный вариант. Другое написание

simplissime

I found the roots for n^2 - n + 1 = 0 using the quadratic equation to be [SQR (3) i + 1]/2 and [SQR (3) i -1]/2. Why did you use only delta?

@onlineMathsTV

11 ай бұрын

It is used just to know if the quadratic equation will give imaginary or real roots. It is a formula know as the "discriminant factor".

bro this math problem is just for grade 7 in my country

Oui

cube root of 2 ans

Giải bằng nhân tử hoặc giải bằng phương trình bậc 2 theo delta

@onlineMathsTV

11 ай бұрын

That's another wonderful way out too.

If I can solve it, and I know I am not olympiad level, it is not an olympiad question. Too easy for that.

-1 is one answer. 1 - (-1) = 1 + 1 = 2. The other answer is 2^(1/3). 4 - 2 = 2.

@onlineMathsTV

10 ай бұрын

Very correct ma. Bravo 👍👍👍 Respect sir 🙏🙏🙏

This is IMO only on Mars. On Earth is just a very simple ecuation.

3fois2

Faurmidable!Excellent

@onlineMathsTV

11 ай бұрын

Thanks a million sir.

@gkwugqbfig2vjg332

11 ай бұрын

Merci