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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.
You are such a good teacher with clear solutions , thanks
😀
Nice. Simple procedure though can be solved by other way.
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.
Such a methodical teacher! Thanks
You are a good teacher❤❤
Задание интересное!
Very clever
Thanks... I think.... it's long solution..... I admitted that you are excellent at the maths .
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.
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
Thanks❤
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
Cool👍
Thank you very much!!
Sole :
X cube - y cube = xy + 61
38
16, 81.
И здесь решается путём подбора в уме без бумаги и карандаша.
Les racines complexes x=(97±63i√ 3775)/2
👍❤, but 3775=25×151 =>
=> x=(97±315i×sqrt(151))/2
1
А теоремой Виетта у вас не пользуются?
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
When you know, that ab=6, you should remenber that a+b=5. The rest is easy.
2,-2,2i,-2i
16
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.
X=16
When I asked Chatgpt, x is about 32.86.
Можно просто 5 возвести в четвертую степень
X16
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
What abt x=16or 81
No leave
Olympiad time over .
Африканец с аналитикой молодец.
Solo entiendo el español.
81=97-16
Очень четкий и грамотный ответ. Браво-бровисимо.
Way too easy to be a Math Olympiad question.
nought divided by two ? That is CONFUSING to an idiot such as me
Меньше десяти секунд на решение этоц олимпиадной задачи.
😂😂😂😂😂
×=16
What about x = 81?
X=81
Х=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.
very time consuming. Sovle this intuitively guys.
Too complicated for my 73 yr old brain to comprehend
🎉🎉🎉😂😂
x=16
What about x = 81?
太複雜了
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
What about 81?
X=16
16
What about 81?
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?