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Great one, by the way you have beautiful hand writting. It is fun to watch you! @18:40 It might be best to leave ab as it is, and solve a + b = 5 and ab= 44 or ab= 6 you will get (a,b)= (2,3) (3,2) and substitute to the original. Less addition
Even logisch nadenken... X kan om te beginnen niet gelijk zijn aan 0 X kan ook niet groter zijn dan 97 Hierdoor blijft alleen 2+3=3+2=5 over => X=16 en/of 81 Zonder veel poespas
X can not be greater than 97 because otherwise 4th root of 97-X would result in an imaginary value. Only three integers powers of four are less than 97. 81, 16 and 1 substituting it looks like X equals 81 and X equals 16 both give an answer of 5 for he original equation.
I think it will be easier if you put x=a^4 then move (a) to other side of equation then raise both sides to power of 4 then simplify. You will get a^4 + 10 a^3 + 75 a^2 + 250 a + 264 = 0 (a+2)(a+3) (a^2 + 5 a + 44) =0 a = -2 -> x = (-2)^4 =16 a=-3 -> x = (-3)^4 = 81
@@vaibhavmittal6442Cierto. Las ecuaciones son como la foto del escenario de un crimen y los simplistas buscamos la solución evidente que no siempre es tan fácil. 2+3 o 3+2 dan 5 (otras opciones pero pocas viendo el escenario/ecuación). El procedimiento de resolución del profesor es impecable por abarcar otras posibilidades no tan fáciles como esta.
@@vaibhavmittal6442 Imaginary solutions are excluded because of the use of the root sign. So X must be between less than 97 but greater than zero. If you were to solve this graphically with the sum of two functions equaling five. You would see that there are two functions with curves going in the opposite direction. This first function rises in a curve from x=0 and y=0 slowly x=1 y=1; x=16 y=2; x=81 y=3; x=256 y=4 while the other falls in a similar curve x=0 y
Nice solution but presentation is way too detailed and time consuming. I'm sure mose viewers can see where the various reorginizations, sums and factoring, etc can be done in one line (two at the most). Good presentation but work on brevity please.
16? Сумма не превышает 5. Числа целые. От 0 до 3, так как 4⁴>97,. а(0...3) корень 4 степени из разности 97-а⁴ должен давать Целое число при извлечении 4 степени. Такое число 2 и 3 Следовательно х=2⁴=16, х=3⁴=81
When we have numbers 0,1 to infinite, why we have to substitute numbers with alphabets. It looks so stupid. May be are giving job opportunities for maths teachers.
Great one, by the way you have beautiful hand writting. It is fun to watch you!
@18:40 It might be best to leave ab as it is, and solve a + b = 5 and ab= 44 or ab= 6
you will get (a,b)= (2,3) (3,2) and substitute to the original. Less addition
You are such a good teacher with clear solutions , thanks
😀
Simple solution.
1. Given a + b = 5
2. Test using a=3 and b=2
Gives x = 81
Yes I believe to your solution is the same mine
thats guess and check, if the value is a decimal or irrational, that wont work
@@herissmon9878 X=16 and X=81
Even logisch nadenken...
X kan om te beginnen niet gelijk zijn aan 0
X kan ook niet groter zijn dan 97
Hierdoor blijft alleen 2+3=3+2=5 over
=>
X=16 en/of 81
Zonder veel poespas
Pero eso es champear utilizando cualquier número en el exámen de seguro te va pedir eso te va pedir una solución lógica
X can not be greater than 97 because otherwise 4th root of 97-X would result in an imaginary value. Only three integers powers of four are less than 97. 81, 16 and 1 substituting it looks like X equals 81 and X equals 16 both give an answer of 5 for he original equation.
Nice. Simple procedure though can be solved by other way.
I think it will be easier if you put x=a^4 then move (a) to other side of equation then raise both sides to power of 4 then simplify. You will get
a^4 + 10 a^3 + 75 a^2 + 250 a + 264 = 0
(a+2)(a+3) (a^2 + 5 a + 44) =0
a = -2 -> x = (-2)^4 =16
a=-3 -> x = (-3)^4 = 81
Such a methodical teacher! Thanks
You are a good teacher❤❤
Right idea but too long démonstration .for exemple when you have a+b=s & ab=p we go directly to the équation t^2-st+p=0 and so many others quick steps
Hi thanks but I find a easy solution. No need to so long solution
Anche non capisco perché ha fatto così
Pls show it bec this is so complicated
I have solved in less than 3 minutes you can watch on Math_java CZcams channel@@olgaa8310
@@olgaa8310there is no margin on which he could write it.
This long solution is for you to learn how to solve those problems but with higher numbers
Very clever
Thanks... I think.... it's long solution..... I admitted that you are excellent at the maths .
Задание интересное!
Cool👍
Thank you very much!!
Thanks❤
One could have checked 2 and 3 in the beginning.
Sole :
X cube - y cube = xy + 61
Les racines complexes x=(97±63i√ 3775)/2
👍❤, but 3775=25×151 =>
=> x=(97±315i×sqrt(151))/2
When you know, that ab=6, you should remenber that a+b=5. The rest is easy.
16
Solution by insight
2+3=5, x=16
3+2=5, x=81
It's not given that x is only a whole number it can be fractional nd if x is fractional a and b will also be fractional
@@vaibhavmittal6442Cierto. Las ecuaciones son como la foto del escenario de un crimen y los simplistas buscamos la solución evidente que no siempre es tan fácil. 2+3 o 3+2 dan 5 (otras opciones pero pocas viendo el escenario/ecuación).
El procedimiento de resolución del profesor es impecable por abarcar otras posibilidades no tan fáciles como esta.
@@rosariobravo9165 yeah it's true but we cannot get all the solutions
@@vaibhavmittal6442 Imaginary solutions are excluded because of the use of the root sign. So X must be between less than 97 but greater than zero. If you were to solve this graphically with the sum of two functions equaling five. You would see that there are two functions with curves going in the opposite direction. This first function rises in a curve from x=0 and y=0 slowly x=1 y=1; x=16 y=2; x=81 y=3; x=256 y=4 while the other falls in a similar curve x=0 y
2,-2,2i,-2i
What abt x=16or 81
No leave
Nice solution but presentation is way too detailed and time consuming. I'm sure mose viewers can see where the various reorginizations, sums and factoring, etc can be done in one line (two at the most). Good presentation but work on brevity please.
81=97-16
Очень четкий и грамотный ответ. Браво-бровисимо.
А теоремой Виетта у вас не пользуются?
When I asked Chatgpt, x is about 32.86.
38
Чому не використовуєте теорему Вієта?
И здесь решается путём подбора в уме без бумаги и карандаша.
1
nought divided by two ? That is CONFUSING to an idiot such as me
Way too easy to be a Math Olympiad question.
16, 81.
Можно просто 5 возвести в четвертую степень
Olympiad time over .
X16
X=16
X=81
Too complicated for my 73 yr old brain to comprehend
Х=81 .
Меньше десяти секунд на решение этоц олимпиадной задачи.
Африканец с аналитикой молодец.
16? Сумма не превышает 5. Числа целые. От 0 до 3, так как 4⁴>97,. а(0...3) корень 4 степени из разности 97-а⁴ должен давать
Целое число при извлечении 4 степени. Такое число 2 и 3 Следовательно х=2⁴=16, х=3⁴=81
Solo entiendo el español.
very time consuming. Sovle this intuitively guys.
When we have numbers 0,1 to infinite, why we have to substitute numbers with alphabets. It looks so stupid. May be are giving job opportunities for maths teachers.
x=16
What about x = 81?
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太複雜了
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×=16
What about x = 81?
А почему a^4 + b^4 = 97?🙄🤔
a + b = 5
Много ненужных подробностей!При решении!
X = {81,16}
Non è chiaro può spiegare in altro modo?
16
X=16
16
16
16
97-x must be higher than 0 ; 97-x must be from N; so if x=81 we found the solution; This way is very quick.
16
What about 81?
16
What about 81?
16
What about 81?