I enjoyed your work and your explanation. Excellent and well done! These problems can be long and it took nearly three pages for this one! Lol Sometimes it feels like you're going down a math rabbit hole with no end but in the end when you do reach a solution (s) it's all good.
لغة الرياضيات لغة عالمية موحدة كقانون كرة القدم حقيقة ما اجمل الرياضيات مع الوضعيات المعقدة التي تبحر بك في اعماق التفكير لحلها كنت محبا لهذه المادة والحمد لله افادتني في الحياة
تماماً! لغة الرياضيات لغة عالمية توحدنا جميعاً، مثل قوانين كرة القدم. إنها تأخذنا في رحلة عميقة من التفكير لحل التحديات المعقدة. سعيد أن هذه المادة أفادتك في حياتك. الرياضيات حقاً رائعة! 😊📊
@@DanielDimov358 If you have two quantities a and b then their average is ½(a + b). Since a and b are equidistant from their own average, you can get the original quantities back by adding half their difference ½(a − b) to their average and by subtracting half their difference from their average. That is, we have a = ½(a + b) + ½(a − b) b = ½(a + b) − ½(a − b) The average of x² and x² − 6x + 18 is half their sum, which is x² − 3x + 9 = x² − 3(x − 3) and their difference is x² − (x² − 6x + 18) = 6x − 18 = 6(x − 3) so half their difference is 3(x − 3). Therefore, we have x² = x² − 3(x − 3) + 3(x − 3) and x² − 6x + 18 = x² − 3(x − 3) − 3(x − 3) Consequently, the product x²(x² − 6x + 18) can be written as (x² − 3(x − 3) + 3(x − 3))(x² − 3(x − 3) − 3(x − 3)) and applying the difference of two squares identity (a + b)(a − b) = a² − b² this gives (x² − 3(x − 3))² − 9(x − 3)² or (x² − 3x + 9)² − 9(x − 3)²
Não acredito que o melhor professor do mundo tenha uma visão de primeira, para saber que o caminho é este aplicado nesta questão.(I don't believe that the best teacher in the world has the first-class vision to know which way is applied to this issue.)
The correct answer is: $x = 0$ Explanation: In the previous responses, we found that the equation $x^{2}+(\frac {3x}{x-3})^{2}=16$ has only one solution, which is $x = 0$. This is because when we substitute $x = 0$ into the equation, both terms on the left-hand side become zero, resulting in the equation being satisfied. Therefore, $x = 0$ is the only value of x that satisfies the equation $x^{2}+(\frac {3x}{x-3})^{2}=16$.
Never ending marathon mathematics and brain 🧠 puzzled stories ever. Einstein newton and all superb mathematicians brain to be needed to understood not like me the stupid one..not getting any sweet juice extract from your mathematics, all energies i have lost to get it understood sir .really sir you've the genius brain and you're great.❤❤❤after this life i shall pray to God ,make me genius like you.❤❤❤❤❤
Parece equivalente a un polinomio de 4to grado, entonces habrian cuatro posibles valores de x X^4 -2X^3-6X^2+32X -16=0 es equivalente al problema propuesto. Un valor real obtenido por metodos iterativos seria 0,56895 con error no superior a. 0, 0006 😂😂😂
Too long explanation and you should have switched to the quadratic equasion earlier, it was inevitable and as far as I know there is no negative square root, because any negative number squared gives a positive number, and a positive number squared is anyway positive
If I watched a few videos like this, I would be mentally ill. 😂😂😂
Me and you my friend, me and you!
And the biggest question is when is this used in the real world?😅😅😅
I enjoyed your work and your explanation. Excellent and well done! These problems can be long and it took nearly three pages for this one! Lol Sometimes it feels like you're going down a math rabbit hole with no end but in the end when you do reach a solution (s) it's all good.
x^2 + (3x/x-3)^2 = 16
x^2 = 16 - (3x/x-3)^2
x^2 = 4^2 - (3x/x-3)^2
(4^2 - (3x/x-3)^2 - difference of squares)
x^2 = (4 - (3x/x-3))(4 + (3x/x-3))
After simplifying the expressions in the parentheses...
x^2 = (x-12/x - 3)(7x - 12/x - 3)
Using polynomial division...
x^2 = (1 - (9/x-3))(7 + (9/x-3))
Then let 9/x - 3 = a
From this we can express the x = (9 + 3a)/a
And we can substitute in the equation to get...
((9 + 3a)/a)^2 = (1 - a)(7 + a)
(9 + 3a)^2/a^2 = -a^2 - 6a + 7
(9 + 3a)^2 = a^2(-a^2 - 6a + 7)
Expanding the parentheses we get...
9a^2 + 54a + 81 = -a^4 - 6a^3 + 7a^2
a^4 + 6a^3 + 2a^2 + 54a + 81 = 0
a^4 + 8a^3 - 2a^3 + 9a^2 + 9a^2 - 16a^2 + 72a - 18a + 81 = 0
a^4 + 8a^3 - 9a^2 - 2a^3 - 16a^2 - 18a + 9a^2 + 72a + 81 = 0
a^2(a^2 + 8a + 9) - 2a(a^2 + 8a + 9) + 9(a^2 + 8a + 9) = 0
(a^2 + 8a + 9)(a^2 - 2a + 9) = 0
Roots of first equation are:
a1 = -4 + √7
a2 = -4 - √7
Roots of second equation are:
a3 = 1 + 2√2i
a4 = 1 - 2√2i
Using the roots of the first equation...
x = 9 + 3(-1 + √7)/-4 + √7 = -1 - √7
x = 9 + 3(-1 - √7)/-4 - √7 = -1 + √7
...after multiplying by the conjugate.
Very long and unnecessary I know, however it is the way I solved it and I wanted to share it.
Di
..
Di
..
I did this kind of maths about 40 years ago. Thanks for the reminder son.
Please always make your solution simple, to the subject interesting to all, first clear the squares and solve within a minute
Nice solution specially how got the (x-3) out of 6x^3+18x^2, neat trick.
ㅣ11
لغة الرياضيات لغة عالمية موحدة كقانون كرة القدم حقيقة ما اجمل الرياضيات مع الوضعيات المعقدة التي تبحر بك في اعماق التفكير لحلها كنت محبا لهذه المادة والحمد لله افادتني في الحياة
اكره مااكره الرياضيات وبسبب الرياضيات لم اصل لاهدافي وطموحي بالتعليم حسبي الله ونعم الوكيل
تماماً! لغة الرياضيات لغة عالمية توحدنا جميعاً، مثل قوانين كرة القدم. إنها تأخذنا في رحلة عميقة من التفكير لحل التحديات المعقدة. سعيد أن هذه المادة أفادتك في حياتك. الرياضيات حقاً رائعة! 😊📊
I prefer to get rid of fraction first, then solution will be of 2 minutes only
Would have been way faster and easier. So much less time to multiply through then gather terms.
Yes,I agree
C'est tres long ca se fait dans 3ou4 ligne . Tu n as qu'à la donné à un Marocain
Или българин@@jirah5397
😂❤@@Ron_DeForest
The solution become.complicated,rather than simplfied😮
It's a troubled solution.
Kafa ütülemek matematiği hiç sevmem
Binomial triangle can solve the equation in just few lines . You like extra sheet
A different approach which does not require a substitution and which does not require having to deal with fractions starts by multiplying both sides by (x − 3)² to get rid of the fraction. We can then proceed as follows
x²(x − 3)² + 9x² = 16(x − 3)²
x²(x² − 6x + 9) + 9x² = 16(x − 3)²
x²(x² − 6x + 18) = 16(x − 3)²
(x² − 3(x − 3) + 3(x − 3))(x² − 3(x − 3) − 3(x − 3)) = 16(x − 3)²
(x² − 3x + 9)² − 9(x − 3)² = 16(x − 3)²
(x² − 3x + 9)² − 25(x − 3)² = 0
(x² − 3x + 9 + 5(x − 3))(x² − 3x + 9 − 5(x − 3)) = 0
(x² + 2x − 6)(x² − 8x + 24) = 0
x = −1 + √7 ⋁ x = −1 − √7 ⋁ x = 4 + 2i√2 ⋁ x = 4 − 2i√2
I would have done same 👍🏻
You're also a great genius ❤❤❤
More simpler
Where does line №4 come from?
@@DanielDimov358 If you have two quantities a and b then their average is ½(a + b). Since a and b are equidistant from their own average, you can get the original quantities back by adding half their difference ½(a − b) to their average and by subtracting half their difference from their average. That is, we have
a = ½(a + b) + ½(a − b)
b = ½(a + b) − ½(a − b)
The average of x² and x² − 6x + 18 is half their sum, which is x² − 3x + 9 = x² − 3(x − 3) and their difference is x² − (x² − 6x + 18) = 6x − 18 = 6(x − 3) so half their difference is 3(x − 3). Therefore, we have
x² = x² − 3(x − 3) + 3(x − 3)
and
x² − 6x + 18 = x² − 3(x − 3) − 3(x − 3)
Consequently, the product x²(x² − 6x + 18) can be written as
(x² − 3(x − 3) + 3(x − 3))(x² − 3(x − 3) − 3(x − 3))
and applying the difference of two squares identity (a + b)(a − b) = a² − b² this gives
(x² − 3(x − 3))² − 9(x − 3)²
or
(x² − 3x + 9)² − 9(x − 3)²
Yeeeeee my brain already bursted🤣🤣🤣
😂
How did you know😮
I prefer to take the square root first and then expand with x-3. This is faster.
too long solution that's why many of us ignored Maths . From your side, excellent potential !
Please give a sense to those x and numbers. Be realistic. Don't speak in signs. Unless you are hiding something.
Excellent. Straight to the solutions. Well done!
Zo‘r
In Turkiye, in university enterance examinations, you have only 1 or 2 minutes to solve this
Não acredito que o melhor professor do mundo tenha uma visão de primeira, para saber que o caminho é este aplicado nesta questão.(I don't believe that the best teacher in the world has the first-class vision to know which way is applied to this issue.)
Как прекрасен язык математики. Всё понятно, подробно объясняно. Учитель супер. Спасибо за ролик.
This is crazy!
Clumsy solution. You try to over complicate the solution.
Too long way and time
Good evening ma. Pls i need help in advance level math and physics pls.
The ưay you solve this equation sis SO LONG.
Pourquoi tu nous dis que racine carré de I est égal encore à i? Ça n'a pas de sens. Il y a un problème avec le résultat à la fin
That is also how learning german will treat you as bigginer.
All these hours, just only to find X 😂
The correct answer is: $x = 0$
Explanation: In the previous responses, we found that the equation $x^{2}+(\frac {3x}{x-3})^{2}=16$ has only one solution, which is $x = 0$. This is because when we substitute $x = 0$ into the equation, both terms on the left-hand side become zero, resulting in the equation being satisfied. Therefore, $x = 0$ is the only value of x that satisfies the equation $x^{2}+(\frac {3x}{x-3})^{2}=16$.
X2( x3)2=16X yes and nos
(x-3). =^ ./.
I really like his explainations! 10 of 10 again. Thank you!
Im not a verygood mathematecians. But i know how to solve problems.in algebra.and calculus.
No wonder I was failing maths
Did the teacher seriously expect me to memorise all this 😳
It can be solved by converting x to a trigonometric function.
(x/4)^2 + (3x/(4(x-3)))^2 = 1
x/4 = cos
3x/(4(x-3)) = sin
16(cs)^2 - 18cs - 9 = 0
Why does algebra have such complications and confusing sequence to solve the problem?😂😂
Hope this can be useful in real life
😂😂😂
Never ending marathon mathematics and brain 🧠 puzzled stories ever. Einstein newton and all superb mathematicians brain to be needed to understood not like me the stupid one..not getting any sweet juice extract from your mathematics, all energies i have lost to get it understood sir .really sir you've the genius brain and you're great.❤❤❤after this life i shall pray to God ,make me genius like you.❤❤❤❤❤
Mbledh e zbret ate q t jep mendja pa terrible fikse
E(x)=(x²+mx+n)(x²+px+q), m,n,p,q€Z
So the underroot of negative one is i, how about the underroot of another negative number?
Thank you. very nice solved equation.
The secret to solving the equation is formulating it into a product of two quadratic expressions that gives zero
Too long way method.
Mmh, till tomorrow 😅😅
Très longue comme méthode
You forget the square on i for the first solution 😅
ТА ЧТО ЗДЕСЬ РИШАТЬ,ЛИХКО И ПРОСТО ,КАК НА ГОРШКЕ ПОСИДЕТЬ🪺
Why al zebra unknown vs unknown.
I don’t understand it. First you need to explain what are 2 and x represent
حين كنا ندرس في الثانوي لا يمكن الانطلاق الا بمجموعة تعريف اي استثناء أن يكون x#3 ضرورية قبل الانطلاق
great
Jesus!
Ne kadar sacma bi soru
You missed that x not allowed 3
Rien que d'erreur
I am great sorry to you! why do you take 16 minute for 1 question? Why you make it coplex?
10
Solution lente
4
4
mali yong sulution, Pinaha ba mali naman
Long methods of solution.
What about short method sir?
Mamma mia 😢
،faute
So long a letter
Para que sirve eso, si no sabe para que es
COMPLICADO
MAS É ORGANIZADO
C'est une identité remarquable ❤
Result same
Aare vaai itni si sota math aur kitna lomba korega??
Amna kitu umetupereka op
Parece equivalente a un polinomio de 4to grado, entonces habrian cuatro posibles valores de x
X^4 -2X^3-6X^2+32X -16=0 es equivalente al problema propuesto.
Un valor real obtenido por metodos iterativos seria 0,56895 con error no superior a. 0, 0006 😂😂😂
C 1.4 hrs or 84 minutes.
I no 😂
Very nice ✅
Thanks ✌️
Umekosea APO
Impressionante
My brain just turned to mush after watching this🫠
It's so simple
X-x/3-1=0
❤❤❤❤❤❤❤❤❤❤
nice
Spreco di carta
Too long explanation and you should have switched to the quadratic equasion earlier, it was inevitable and as far as I know there is no negative square root, because any negative number squared gives a positive number, and a positive number squared is anyway positive
1/10..?
Х=2
# 30 #
This shows us how long, hard and tiresome it is to come up with a constitution..Dont blame your government too much😅
👍
👍👍👍👍
4-
Good
Thanks
Nice
Thanks
Excellent
Thank you so much 😀
前面都看懂了，后面根号里公式不记得了，为什么-1开根号变成i😅
Beautiful
Thank you very much
Make people understand 😅😅😅😅😅😅😅😅😅
Почему в ответе Вы сократили на 2..????
Так нельзя!!!
Ой, раздули из простого решения целое математическое расследование