” Ｘ² ーＸ³ ＝１２”　 １st　left　 →　Ｘ² ーＸ³ ＝ Ｘ²（１ーＸ）　　　　 ２nd right　→　１２＝４×３＝ ４×（１＋２) ）＝ ( -2) ² ×（１ー ( -2) ） ３rd　X＝ -2

@modernsabri6654

5 ай бұрын

The equation third degree have three roots (-2) not enough?? So he gets another two roots, Imaginary roots.😊

@dajo3032

5 ай бұрын

Well done 👏

@todaaki4109

5 ай бұрын

＞@@dajo3032 Thank you so much.

@mohammadhosseinshahidi7330

5 ай бұрын

I solved it the same as you

@zahidulislam2578

5 ай бұрын

I have an another easy way to solve it. And i prove it easyly

Excellent math question and smart expanation. Muchas gracias

Marvelous.

Inspiring

well done sir , I learnt a lot

How nostalgic for school! I still remember the amazement when I realized that I was coming to the solution and the joy when I found it. It was just an equation in the end, but for me it was like conquering the world

Very good exercise, thank you.

Great explanation

The last 2 lines on the first column had errors, the last, serendipitously 'correcting' the second to last. In the second to last you forgot to make the 2^3 positive inside the parenthesis. In the last you forgot to make (from the erroneous equation) the x^3 negative. So erroring twice the 'corrected' the equation on the last line. So just erase the second to last equation and your good! All is well that ends well. You passed the test, making 2 bad operations!!!!

@soundsoflife9549

5 ай бұрын

Yeah ! I was wondering how x^3-2^3=x^3+2^3 !

@proislam-co6pg

5 ай бұрын

only the second last is wrong

@markdagley4213

5 ай бұрын

That depends on how you look at it. To go from the second to last to the last is wrong but it corrects the second to last wrong by being wrong. So if you remove the second to last, only then is the last right.@@proislam-co6pg

@uygarbocutoglu4465

5 ай бұрын

luckly i decided to read the comments before judjing my retirred maths abilities

@ceccilioantoniosilvaayala4127

3 ай бұрын

Cuando abris paréntesis por primer vez, 2 al cubo pasa a positivo.

It's pretty clear right from the start that x has to be negative, otherwise the right term would be

@jagzeyfn

2 ай бұрын

what about the complex solutions

@LarsEllerhorst

2 ай бұрын

@@jagzeyfn Whatever complex number you put into x, it will never be equal to 12.

@AEditor.0

Ай бұрын

You can find it up to a certain number by trial and error. But what do you do when asked for a larger number?

@LarsEllerhorst

Ай бұрын

@@AEditor.0 Sure, most of such equations needs to be calculated properly, but knowing how such functions progress helps you with a good prediction where the solution should be. It will be tricky if the result is a complex value.

Nice job

Thank you. Sir.

If the goal of the olympiad is to solve the problem quickly, I would apply numerical theory first. It’s obvious that x^3 is more than x^2 when x is positive. So the equation can only be solved with x

WOW! I LIKED THIS VIDEO...GOD BLESS YOU...

Thank you sir

good 😍😍

By finding that (-2) is a real root we can use long division X^3-X^2+12/X+2 = X^2-3X+6 and then get the imaginary roots. Thank you sir for what you do. 14:2

Much appreciated. There' s also a simpler way to come up with the answer. If factoring out x^2 , then we have: x^2 (1-x)= 12 There would be just one possible choice left out of three positive pair factors of 12 that includes a perfect square. i.e. 4 and 3. So: x^2= 4 and (1-x)= 3 The only common answer of the above two equations is then: x=-2

@onlineMathsTV

4 ай бұрын

Bravo!!! you are good at it.

@leylaaghazadeh9185

4 ай бұрын

Thank you sir 🙏

@randymills2660

4 ай бұрын

This is just a guess and check method. The preferred way to solve any polynomial equation is to solve for 0 first.

@Roman_Ray

3 ай бұрын

Honestly, knowing that x has to be negative is a dead giveaway, cos it can't be positive (cos subtracting a cubed number (bigger) from the same but squared (smaller) number yet still getting a positive result => x has to be negative), and we also know it's not "1". Hmm what number comes next?

@Drunkenmaster632

3 ай бұрын

​@@randymills2660Neither is that a guess and check not is solving for 0 is the preferred way

Excellent

I love it. Brilliant ❤

... Good day sir, We could also solve the Complex part as follows: X^2 - 3X + 6 = 0 [ Applying Completing the Square ] ... (X - 3/2)^2 - 9/4 + 24/4 = 0 ... (X - 3/2)^2 = - 15/4 ... X - 3/2 = +/- SQRT(- 15/4) ... X - 3/2 = +/- SQRT((- 1)* 15/4) [ Applying i^2 = - 1 ] ... X - 3/2 = +/- SQRT(15/4 * i^2) ... X2.3 = 3/2 +/- SQRT(15) * i / 2 ... X2 = (3 + SQRT(15) * i) /2 v X3 = (3 - SQRT(15) * i) / 2 ... X2 and X3 are COMPLEX CONJUGATE SOLUTIONS, but are certainly NOT IMAGINARY SOLUTIONS, because in general Z = A + B * i is always COMPLEX, and when A = 0, then Z = B * i is both COMPLEX as IMAGINARY! In short : The set of Imaginary numbers (Z = B * i) is a SUBSET of the set of Complex numbers (Z = A + B * i ) ... great presentation by the way sir, and thanking you for your instructive math efforts ... best regards, Jan-W

you made a mistake. to jump from x^2-2^2-x^3-2^3=0 to (x^2-2^2)-(x^3-2^3)=0 is very wrong. it should have been (x^2-2^2)+(-x^3-2^3)=0 and then only you could have proceeded to (x^2-2^2)-(x^3+2^3)=0

@seekingthelovethatgodmeans7648

Жыл бұрын

yes, a mistake... the intention seems to be "we will group" but the parens are wrong. The way, say, SyberMath shows the intention to group is by underlining first.

@richesekanem4525

5 ай бұрын

There was a mistake but he recovered it

@alexrozenbom3430

5 ай бұрын

i noticed it too.

bommmbaaaa!!!! que fantástico, muy bien profesor. su didáctica es muy clara y enseñadora. muchas gracias

FANTASTIC😍😍😍😍😍😍😍😍😍😍

When some terms were regrouped and put inside brackets the second line from the bottom left isn't correct but the line below is correct. It wasn't properly explained as to what was going on at that point. Someone who may be a bit weak in their math skills might get confused about that part and why the sign was changed from - to +.

@user-xk9gz7ey3k

2 ай бұрын

YES,my brother,he has bigggggggggggg fault and his solution is completly fault

Nice. I would use a formal method to solve this problem: 1) observe -2 is a real root. 2) divide x^3-x^2+12 by x+2, the quotient then is Q(x)=x^2-3x+6, now it's quite easy to find other two complex roots of Q(x)=0.

@georiashang1120

5 ай бұрын

that quotient method is really usefull solving high power equations.

@hn4806

5 ай бұрын

Yes, my self, I'd always do that way because, in f(x)=0 where f(x) of power of 3 (let's denote it with f3(x)) must be in f1(x)*f2(x) to be solved. If the second f2(x) is factorized to f1(x)*f1(x), then 3 solutions all real right away. If not, f2(x) gives 2 solutions from the formula, either real or imaginary. That way we don't need x**3 +/- y**3 = (x +/- y)(x**2...) formula. The question is how fast you find the number for the f1(x) i.e. (x - ?). Typically the number is small, 1, 2, 3 or -1, -2, -3. Seldom odd case such as -7. I want to think of a systematic way to come up with this number, rather than applying try-and-hit way...

@uthoshantm

5 ай бұрын

Well, that's assuming you can pick up the -2 by inspection.

@emremokoko

5 ай бұрын

no, you dont need inspection. Descartes' Rule of Signs tells you that there IS one negative root. They can only be -1, -12, -2, -6, -4, -3. Try the edge cases first, that is -1 and -12. You see that it must be closer to -1. Try -2. That works. @@uthoshantm

@kimba381

5 ай бұрын

@@uthoshantm In this case its pretty easy. x is clearly negative, and x^2 is a factor of 12, must be 4. If it had been, say 10 rather than 12, whole different kettle of fish.

Thanks for your efforts

Excelente

X = -2 X² * ( 1 - X¹ ) = 12 ( para dar esse valor tem que ser 4 * 3 = 12 Então, (-2)² - (-2)³ = 12 +4 + 8 = 12 Bingo from Brazil!!!!

@qwe-my3hu

5 ай бұрын

인도늠들이 수학을 잘한다고 들었는데 참말이네요..그런데 그 지경으로 살고 있는게 이상하네요

@jaylooppworld381

2 ай бұрын

Wrong

@tistrya-424

26 күн бұрын

exactly, thats what i wanted to write here - Noice

wow. that was really cool! thank you for your videos

@onlineMathsTV

Жыл бұрын

Glad you like it, you welcome

Explained in very good way. Thank you so much!

Good job

По теореме о рациональных корнях уравнения можно сразу найти корень х=-2, затем поделить исходный многочлен на х+2, а дальше решить оставшееся квадратное уравнение. Стандартная школьная задача, что тут олимпиадного? :)

@dough9512

4 ай бұрын

But division by zero is undefined?😮

@Xingzi786

Ай бұрын

Olympiad finds gifted high school students. (it's tough) Its an easy Olympiad question. It's still a tricky question for grade 10 Student.

Согласен с @gorbachevaol. Имплементация алгоритма Горнера, подчеркнула бы структурную инвариантность, обеспечивает внедрение дифференциальных операторов в рамках алгебраического контекста. Так получаемые корни уравнения имеют больший математический смысл, по моему

Very good explanation. Thank you.

Amazing!

Отлично так минус на плюс заменил, бро! 👍🏻

@dj_multiple_one

5 ай бұрын

я тоже не понял как он так

@broomska1

5 ай бұрын

​@@dj_multiple_oneДа никак. Просто словами проговорил, что типа так неправильно. И в следующей строке написал, как надо. Но неверное представление не убрал.

@mallonamolloly2569

Ай бұрын

@@broomska1 Вот то, что не убрал - это большущий косяк! Вероятно у них в колхозе так учат.

х^3-х^2-12=0 Челочисленные корни являются делителями 12. х=-2 является Схема Горнера (или деление многочлена на многочлен) и получаем квадраратное уравнение с D

@hannukoistinen5329

5 ай бұрын

What!!! Write normal letters or shut up and stay in Soviet union!!!

@user-fk8kh4vm8u

5 ай бұрын

@@hannukoistinen5329 retarded yenkee lmao

@Pereseld

5 ай бұрын

@@hannukoistinen5329 I want to stay in Soviet Union)

@broomska1

5 ай бұрын

​@@hannukoistinen5329А причем тут Советский союз?

@cortisol1801

5 ай бұрын

​@@hannukoistinen5329junge, soviet Union ist schon lange vorbei. In welchem Jahr wohnst du?

Fantastic

I love your teaching skills

My solution take only 30 second 😂. I feel very intelligent 😂😂😂 thank you for primary school level olimpic questions 😅😅

@gospelvibes374

2 ай бұрын

😂😂😂

@chrissyday67

15 күн бұрын

Is fthis really for Primary school level? I hope so as I was quite concerned at the fall in scholastic standards

@blue_white1759

15 күн бұрын

@@chrissyday67 this question is easy to answer but you are right. Unfortunately, Every year student standarts are falling down more...

Задача решается за 5 секунд в уме... Вот бы у меня в школьные времена были такие простые задачи))

@mnnkaz0

4 ай бұрын

здравствуйте, а как можно в уме быстро решить? объясните, пожалуйста!

@Kroner108

4 ай бұрын

@@mnnkaz0обратить внимание на 4 + 8 = 12 и на минус в выражении, и просто понять что х = -2.

@professeurkeitagaye3118

4 ай бұрын

C'est bien expliqué mais il fallait préciser l'ensemble dans lequel on travaille dans la question.

@---wb5tt

4 ай бұрын

Да, за 5 секунд, если вы до этого решали схожие примеры....

@swerwolf

4 ай бұрын

@@mnnkaz0 никак... Они все топят за "метод подбора", который на самом деле "метод пальца в небо". "Я угадал, потому что подошло" не равнозначно "я решил".

Great solution, Dear

I like your explication 💭❤️

Перенести все влево и исследовать функцию с помощью производной. Построить график и увидеть одну точку пересечения . Это -2. С помощью проверки убеждаемся , что -2 корень уравнения.

@lopezpablo88

5 ай бұрын

Ingenioso. Y si, hay varios caminos válidos 😃

@Darius-kb9ew

4 ай бұрын

То чувство, когда решил в уме😁

@user-zd6zr5ei6l

4 ай бұрын

Так видно же что x отрицательный, там подбором решается за секунду

@user-iz4yx3oz9m

4 ай бұрын

@@user-zd6zr5ei6l да. Но ещё нужно доказать, что других корней нет.

You made mistake. When you facror out -1, you should have -(x*3+2*2) not (x*3-2*2)

@ignatiuswinarto5968

6 ай бұрын

No need to use a long pocedure to solve that the value of x is -2. Just use simple arithmatic to get the correct answer

@666DomSathanas666

5 ай бұрын

I was looking for a comment like yours, I couldn't be the only one who saw this error.

@fendibasrifendi4229

Ай бұрын

Yup there was an error on factorisation.

EXCELENT

I'm a senior, ill in bed with flu and did this in less than a minute in my head - it's obvious from the equation that either x must be negative then you just need to fins a number that when it's square is added to it's cube yields 12 ( the fact it is negative means that minus the cube of it will become positive) is it not obvious that the number is 2? since 4 + 8 = 12. This is the third 'Olympiad' math question I've looked at this afternoon, being too unwell to do much else and all were easily do-able in my head rather than the long-winded solutions. I recently took a senior cognitive test (annual requirement at my age) and am amazed if this is how students are taught to solve these kind of puzlzles. Maybe I should start a "Granny shows you how" you tube series? 😆 Well I have learned something, I know I am not as quick-witted as I was 50 years ago, but I still have some of my marbles 😊

this guy did 15 min video just to proof that x equals -2 when everyone guessed it in half a minute true legend.

@nelsoneason5822

5 ай бұрын

他是在教思考的““方式”” 所以得用簡單的數字帶您思考 如果今天的常數從原本的12改成64160000或是更多大的數字那就很難30秒解答出來

@nonsencephilosophy

5 ай бұрын

@@nelsoneason5822 fair point. knowledge of the algorithm is always the most powerful weapon

@nelsoneason5822

5 ай бұрын

@@nonsencephilosophy wow you are a nice guy+9999999

2乗の数から３乗数を引いてプラスになる数はマイナスの数であると解る。-１では12ににならない。-２で即+４と-８とで１２と解る。

Thank you, You are an excellent!

You made silly error with the sign of 2 to the power of 3 (line 6 of the solution). Then you made another error in line 7. This is ridiculous ...

@yitzchakgrinboim1989

5 ай бұрын

Plus the question is extremely simple for an Olympiad

@juanjuan-mi4gi

5 ай бұрын

Revise su video antes de mostrarlo....

@khigia984

5 ай бұрын

Good catch, but his 2 wrongs turned out to be right

@AhmedsNjie-hg5du

5 ай бұрын

Bro there's nothing wrong in those steps.. Every step is just awesome

@yitzchakgrinboim1989

5 ай бұрын

@@AhmedsNjie-hg5du dude, it's an easy question, 4+8 us an intuitive solution so you immediately know that one root is -2, then you divide by (x+2) and you solve a quadratic. I don't know why the weird steps..

X^2-X^3=12 X^2(1-X)=4×3 X는 음수가 되어야 함으로 X=-2 이렇게 간단한 문제를 너무 어렵게 푸네요.

Excelente video. Nuevo suscriptor a tu canal. like gran video

With due respect Sir, Just by seeing the equation we can find the answer.. or hit and trial method can also be used.. Of course we will not be able to find complex answers mentally, but they are as it is rejected for the solution unless asked for in the exam. Thank you for sharing this video. Regards 🙏🙏

@daakudaddy5453

5 ай бұрын

You must be Indian. Trial and error method is not real Mathematics. But you guys don't study or care about real Mathematics, nor appreciate it's beauty. To you, finding the answer faster than the other guy in an exam by any means possible is Maths. Higher score is victory. It is not methodical or exhaustive, it's just trick play. Like the difference between a cheap thrill seasonal action film and a timeless classic.

@88kgs

5 ай бұрын

​@@daakudaddy5453 Do something for your frustration, I wish you peace

@rrinfinity4912

5 ай бұрын

​@@daakudaddy5453The method discussed in the video is also nit methodical, in the sense that it would only work for this cases. I guess the most reliable is the cubic formula here or numerical methods, everything else is tricks play. What's the point on insulting every student here when most of them are not even responsible for it? Besides, your criticism of students not being exposed to the beauty of math isn't only common in india but everywhere.

3:42 я не понял, как он превратил х^3-2^3 в х^3+2^3

@bobbadner7975

5 ай бұрын

он ошибся и исправился в следующей строчке.

I like you explanation,it is fantastic

x² - x³ = 12 Let's see, a square and a cube that add/subtract to 12? Well 2 would work if it were a sum, not a difference: 4 + 8 = 12. But wait, we can make that happen just by changing the sign on the 2. x = -2 x² - x³ = (-2)² - (-2)³ = 4 + 8 = 12 Having found a root, the next step is to factor it out and solve the resulting quadratic. x³ - x² + 12 = (x + 2)(x² - 3x + 6) = 0 x = -2 or x² - 3x + 6 = 0 x = 3/2 ± ½i√15 So if you're looking for real solutions, x = -2 is the only one. Fred

Графічно. Побудуємо графіки y=x^2 та y=x^3+12. Вони мають одну точку перетину, очевидно аргумент відємний. Значить рівняння має один корінь. Підбираємо, х=-2. Все !!

@user-fu8zc2co3k

3 ай бұрын

فقط القليل من التخمين بوضع 12=4×3

Love u teacher.. ❤❤

it's easily proofed, that one obvious solution is x= - 2 alternative solution 1: divide x³ -- x² + 12 by x+2 with the so called long division (polynomial division) to find the polynomial of degree 2. solve this quadratic equation to receive two complex solution if needed. alternativ 2: x³ -- x² + 12 = ( x +2)(x² + ax + 6). find the parameter a by multplication, and comparing both sides.

Thank you ❤️

You can simple use Horner for the value x=-2.

Thanks .

That was very nice.

It was great, well done

@onlineMathsTV

3 ай бұрын

Thanks for watching and encouraging Onlinemathstv with your words sir. Much love from us here...💖💖❤️❤️

good.

Nice

@onlineMathsTV

2 ай бұрын

Thanks

This awesome, u just open my understanding to solving this using this unique method. Thanks for this video sir.

@onlineMathsTV

Жыл бұрын

Glad to hear that

x^n+y^n=z^n(n>=3) Fermat's last theorem please!

Thanks so much continue 😅

Nice nice

Felicitaciones por el formidable desarrollo analitico. Sin embargo la solución (x=-2) adviene simplemente por tanteo una vez que te percatas de que DEBE ser un número negativo. Y el proceso mental para hallarla no lleva ni un minuto, sin necesidad de ser una especie de Ramanujan, ni tener un infinitesimo de su talento, por asi hablar

Congratulations

Exceptional ❤

J'ai eu de la chance de trouver plus rapidement ! On remarque que 12 = 3 x 4. Écrivons l'expression x**2 - x**3 = x**2 * (1 - x). Supposons xx*2 = 4 et (1 - x ) = 1 - (-2) , du coup on a bien x = -2 comme solution. (NB '**' signifie ici puissance d'un nombre et * multiplication)

I like your class

@vandemaataram2600

Ай бұрын

Just watch the channel 'Khelo Maths Ke Saath' also. You'll definitely like it. 👍

Bravo, big Bravo

I solved this in 5 seconds thus: 4 + 8 = 12, 4 - (-8) = 12, x = -2. (If only real roots are wanted, long division shows there are no other)

These type of problems in exams, usually have a simple solution that by simple looking can be obtained (for example (-2) is obviously a solution of the problem). Then you can divide the equation by x+2 and easily solve the obtained second order equation for other two roots.

Preferably subtract 12 from both sides ( addition property of equality).

I simply gav that formula in the FNgraph shell as was example program in UUP and saw result.

Some comments suggests, that x=-2 could be found within 10 seconds. And indeed, x=-2 is an obvious answer. But how to prove, that it is the only answer? We all know, that "x^2=4" has not only one answer. He broke the equation down to two: x+2=0 --> first solution 3x-6=x^2 --> potential alternative solution(s) Therefore the remaining question had been, if the second equation can be solved. Or not. And he listed correctly both complex conjugates --- even x2 and x3 are awkward. Well done.

@onlineMathsTV

5 ай бұрын

@KaiUga-ni3hk you just pointed out a very salient point which I found difficult trying to make everyone to understand as far this math challenge is concerned. On behalf of OnlinemathsTV, I really want to say a very big thank you for your deep understanding of what actually prompt Onlinemaths TV to apply this approach that is being questioned by almost everyone here with a better understanding of things. You are good at what you do, maximum respect from everyone here for . Above all, we love you dearly and deeply sir....❤️❤️💖💖💕💕😍😍😍

Another way is to change the equation to like this x^3+2x^2-3x^2+12=0. Then keep factoring

ขอบคุณครับ

Very good!

@onlineMathsTV

5 ай бұрын

Thank you! Cheers!

Very beatiful explained and correctly solved problem. Because of the third degree term,there must be at least three roots for the equation. İf you draw the diagram of this equation in the analytical plane you will see the roots. I personally was not aware of the equation for root calculation and now learned it. Thank you very much for this informative video

@meltembuz7206

4 ай бұрын

Plus wolfram alfa gives the exact same roots for the equation, for ones information,who does not belive the solution.

Good teaching ❤

You prolonged the problem. You could have factored the problem out earlier without going through all those additional steps. But I understand you were trying to show the entire process of thought. Good job.

bem explicado, mais usou uma linha no inicio que não entendi, porque de 4 e 8? eu aprendi de outra forma, pena que eu não sei bem inglês

I think the long way to solve the simple problem like this is not suitable any more. This method makes many many students confused and scared of math.This problem , we don't need to move number 12 to the left to make the equation =0.Simply we do: We keep the left, and change the right to 2 with the exponent 2 plus 2 with the exponent 3.So we have the exact formular for both side. Then we do math on the left side we will have -X = 2 (on the right side). It means X = -2. Two steps only.

因数定理で分解して解きました🎉

Thank you sooooo much.

@onlineMathsTV

2 ай бұрын

You're welcome!

No entiendo porque tantos comentarios negativos. Es cierto que el problema es sencillo para ser de una olimpiada de matemáticas pero nunca dijo de qué nivel es... Además la solución es correcta y hay varias formas de llegar a ella. "Intuir" que -2 es una solución y luego factorizar es fácil pero, para mi, tiene más logro llegar a esa conclusión por una vía matemática. Y en las olimpiadas eso se valora.

@onlineMathsTV

5 ай бұрын

@lopezpablo88, I think you deserve a standing and a clapping ovation from everyone @OnlinemathsTV as far this math challenge comments are concerned, hahahaha... I love it when people criticize and correct other constructively with a deep understanding of the point/s in question. Here, you have shown a deep level of mathematical prowess. Thanks a million for your wonderful contribution to the growth of this platform/channel. We all here love and salute your choice of words and wisdom in handling issues sir. Maximum respect and deep love to you from all of @OnlinemathsTV sir....❤️❤️💖💖💖💕💕😍😍😍.

X^2 - X^3 = 12 X^2(1-x) = 2^2*(1-(-2)) , or X^2(1-x) =(-2)^2*(1-(-2)) If we compare left and right sides of equations, It is obvious, that true version of equation is X^2(1-x) = (-2)^2*(1-(-2)) That is x = -2

I think this way : 1. X must be negative, because if X positive, X^2 X^2 - X^3 never equals 12. 2. Negative but range ? X should be from 0 to -3 (I only consider integer), because -X^3 must 3. Make a try with integer and easily find X = -2. Base on this to form the other equation to find another 2 X.

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*You are the Best!*

Let P(x)= x^3-x^2+12. One can easily verify that x=-2 is a solution of the equation, so (x+2) is a factor of p(x). Use long division we see that p(x)=(x+2)(x^2-3x+6) ....

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