France | Can you solve this ? | Math Olympiad

[@mannmasterm]

You are such a good teacher with clear solutions , thanks 😀

[@arunsanghvi6139]

Simple solution. 1. Given a + b = 5 2. Test using a=3 and b=2 Gives x = 81

[@احمدروضاتی]

Yes I believe to your solution is the same mine

[@herissmon9878]

thats guess and check, if the value is a decimal or irrational, that wont work

[@kimobrien.]

@@herissmon9878 X=16 and X=81

[@yvonneciemniak5957]

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

[@josejutuba5548]

Pero eso es champear utilizando cualquier número en el exámen de seguro te va pedir eso te va pedir una solución lógica

[@ghosh9903]

Nice. Simple procedure though can be solved by other way.

[@E.h.a.b]

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

[@Abby-hi4sf]

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

[@elmereggkioskabequibel6391]

Im watching from Philippines guys it's amazing

[@VIJAYKUMAR-eg3yf]

I'm from India 🇮🇳 it's amazing solution

[@cachotrelles4715]

Buen día. Me costó comprenderlo en su totalidad, pero lo copié para, también, realizarlo paso a paso. GRACIAS!!!

[@theLordsboy]

Such a methodical teacher! Thanks

[@Lemda_gtr]

So clever 🎉

[@احمدروضاتی]

Hi thanks but I find a easy solution. No need to so long solution

[@mariapiapiro3718]

Anche non capisco perché ha fatto così

[@olgaa8310]

Pls show it bec this is so complicated

[@NITian875]

I have solved in less than 3 minutes you can watch on Math_java KZbin channel​@@olgaa8310

[@walczacyrys826]

​@@olgaa8310there is no margin on which he could write it.

[@snowziethepro]

This long solution is for you to learn how to solve those problems but with higher numbers

[@kimobrien.]

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.

[@SusharmaGhosh-t2l]

You are a good teacher❤❤

[@ValentinaYomtov]

Thank you. Exellent! 👏👏👍

[@learncommunolizer]

your welcome 🤗🤗

[@lahcenlamrabet]

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

[@salamoujda3651]

ء@@bravo!

[@ВалентинаКазакова-м3п]

Задание интересное!

[@davidwoodhead1037]

Very clever

[@fireblast3740]

Второе слагаемое сильно режет возможный набор значений. Т.е. корень отрицательным быть не может. Соответственно надо найти такие иксы, при которых корень будет извекаться. Это соответственно 16, 81, 96. 96 сразу отпадает как решение, так как чисто из него корень нормально не получить, а вот 16 и 81 очень прекрасно работают. Соответственно это и есть наши решения. Другая задача - доказать наличие отсутствие других решений

[@에스피-h8t]

Solution by insight 2+3=5, x=16 3+2=5, x=81

[@vaibhavmittal6442]

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

[@rosariobravo9165]

​@@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]

@@rosariobravo9165 yeah it's true but we cannot get all the solutions

[@kimobrien.]

@@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

[@ณรงค์ศักดิ์รักชาติ]

Thanks... I think.... it's long solution..... I admitted that you are excellent at the maths .

[@SocratesAlexander]

One could have checked 2 and 3 in the beginning.

[@Max892-s]

Cool👍

[@learncommunolizer]

Thank you very much!!

[@Yureka-ox5jn]

Thanks❤

[@peterlasser]

×^4 + 4 = 0 ⇔ (x^2 +2i)·(×^2 - 2i)

[@nagarajahshiremagalore226]

Sole : X cube - y cube = xy + 61

[@heikelawin3771]

I try the first numbers: 1⁴ = 1, but 2⁴ = 16 4.wurzel(16) = 2 and 4.wurzel(97 - 16) = 4.wurzel(81) = 3 2 + 3 = 5 finish 😂

[@DiegoPitol-b8n]

Olá professor, o X é igual a 16. Pois, a raiz quarta de 16 = 2, a raiz quarta de 97 - 16 = 81 é igual a 3 e 2 + 3 = 5

[@Ginkobil50]

When you know, that ab=6, you should remenber that a+b=5. The rest is easy.

[@kajalbanerjee8220]

2

[@TWJRPGGamming]

2,-2,2i,-2i

[@xaviersoenen4460]

Les racines complexes x=(97±63i√ 3775)/2

[@rabotaakk-nw9nm]

👍❤, but 3775=25×151 => => x=(97±315i×sqrt(151))/2

[@kajalbanerjee8220]

81

[@Bertin-q3y]

X=81

[@gmeier391]

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.

[@يوسفالبرغوثي-ه3ت]

81=97-16

[@АндрейКожевников-о8й]

Очень четкий и грамотный ответ. Браво-бровисимо.

[@taharbendaya]

- 528 no +528 attention

[@Misha-g3b]

16, 81.

[@bonitokumar4977]

Olympiad time over .

[@DonaldKim33]

When I asked Chatgpt, x is about 32.86.

[@kienbui6262]

1

[@ЕвгенияСтрелец-щ3ш]

Можно просто 5 возвести в четвертую степень

[@doowadiwadi]

Way too easy to be a Math Olympiad question.

[@valeriyabakumov1652]

И здесь решается путём подбора в уме без бумаги и карандаша.

[@sankariraman6453]

What abt x=16or 81

[@sankariraman6453]

No leave

[@АндрейКожевников-о8й]

Африканец с аналитикой молодец.

[@ОлександрДрига-ш5ч]

Чому не використовуєте теорему Вієта?

[@user-cw5ec9hk6lh]

X16

[@Lars_Porsenna]

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

[@sonuok]

very time consuming. Sovle this intuitively guys.

[@kajalbanerjee8220]

16

[@ternatjacques4330]

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.

[@ВикторияМ-й5б]

А теоремой Виетта у вас не пользуются?

[@CS-vm7lq]

Mi mente me dijo que el valor de X es 16

[@ВарданВарданян-ж2ш]

×=16

[@oahuhawaii2141]

What about x = 81?

[@dardoburgos3179]

X= 16. No hace falta explicación.

[@olgaa8310]

Too complicated for my 73 yr old brain to comprehend

[@user-qr7dw4hk6x]

Меньше десяти секунд на решение этоц олимпиадной задачи.

[@yudithmanco9840]

Solo entiendo el español.

[@heniwatisetiono6995]

x=16

[@oahuhawaii2141]

What about x = 81?

[@pholdway5801]

nought divided by two ? That is CONFUSING to an idiot such as me

[@АндрейКожевников-о8й]

Х=81 .

[@khalifauduman5598]

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.

[@ЖалилАширов-д9е]

😂😂😂😂😂

[@이털많고착한남82]

🎉🎉🎉😂😂

[@簡欽慧]

太複雜了

[@ВалентинаКазакова-м3п]

Много ненужных подробностей!При решении!

[@АлексейЧерногубов-с3г]

А почему a^4 + b^4 = 97?🙄🤔

[@oahuhawaii2141]

a + b = 5

[@miracbarsapaydn650]

X = {81,16}

[@mariapiapiro3718]

Non è chiaro può spiegare in altro modo?

[@SidneiMV]

∜(97 - x) + ∜x = 5 0 < x < 97 x = a⁴ 97 - x = b⁴ a⁴ + b⁴ = 97 a + b = 5 (a + b)⁴ = 625 a⁴ + b⁴ + 4ab(a² + b²) + 6a²b² = 625 97 + 4ab(a² + b²) + 6a²b² = 625 (a + b)² = 25 = a² + b² + 2ab a² + b² = 25 - 2ab 97 + 4ab(25 - 2ab) + 6a²b² = 625 97 + 100ab - 8(ab)² + 6(ab)² = 625 2(ab)² - 100ab + 528 = 0 (ab)² - 50ab + 264 = 0 (ab - 44)(ab - 6) = 0 a + b = 5 ab = 6 (a, b) = {(2, 3); (3, 2)} x = a⁴ ∨ x = 97 - b⁴ x = a⁴ = 2⁴ => *x = 16* x = a⁴ = 3⁴ => *x = 81* a + b = 5 ab = 44 t² - 5t + 44 = 0 => complex roots

[@anshumanpanda4962]

16

[@Bertin-q3y]

X=16

[@teomancete5740]

16

[@ДмитрийБелых-к1ю]

16

[@oahuhawaii2141]

What about 81?

[@essa2902]

16

[@nizamibayramov1518]

16

[@oahuhawaii2141]

What about 81?

[@sriindrawati7572]

16

[@oahuhawaii2141]

What about 81?

[@tamarshahverdyan2723]

38

[@SaiPraveen-ss8vj]

16

[@drggayathridevi195]

16