France | Can you solve this ?

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France | Can you solve this ? | Math Olympiad

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Күн бұрын

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Пікірлер: 102

@arunsanghvi6139 8 ай бұрын

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

@user-er9wj9nv8m 8 ай бұрын

Yes I believe to your solution is the same mine

@herissmon9878 8 ай бұрын

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

@kimobrien. 6 ай бұрын

@@herissmon9878 X=16 and X=81

@yvonneciemniak5957 5 ай бұрын

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 4 ай бұрын

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

@Abby-hi4sf 2 ай бұрын

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

@VIJAYKUMAR-eg3yf 6 күн бұрын

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

@mannmasterm 4 ай бұрын

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

@elmereggkioskabequibel6391 10 күн бұрын

Im watching from Philippines guys it's amazing

@ghosh9903 6 ай бұрын

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

@kimobrien. 6 ай бұрын

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.

@Lemda_gtr 22 күн бұрын

So clever 🎉

@E.h.a.b 8 ай бұрын

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

@theLordsboy 8 ай бұрын

Such a methodical teacher! Thanks

@user-ec4ip7bp1n 3 ай бұрын

You are a good teacher❤❤

@davidwoodhead1037 3 ай бұрын

Very clever

@lahcenlamrabet 8 ай бұрын

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 9 күн бұрын

ء@@bravo!

@user-er9wj9nv8m 8 ай бұрын

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

@mariapiapiro3718 6 ай бұрын

Anche non capisco perché ha fatto così

@olgaa8310 6 ай бұрын

Pls show it bec this is so complicated

@NITian875 6 ай бұрын

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

@walczacyrys826 4 ай бұрын

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

@snowziethepro 2 ай бұрын

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

@user-pi2my7vk5j 3 ай бұрын

Задание интересное!

@ValentinaYomtov Ай бұрын

Thank you. Exellent! 👏👏👍

@learncommunolizer Ай бұрын

your welcome 🤗🤗

@SocratesAlexander 2 ай бұрын

One could have checked 2 and 3 in the beginning.

@user-dv8gv3hu4t 8 ай бұрын

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

@vaibhavmittal6442 8 ай бұрын

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 8 ай бұрын

@@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 8 ай бұрын

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

@kimobrien. 6 ай бұрын

@@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

@user-xx3es5de8d 9 күн бұрын

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

@user-ro3pd5dj1z 6 ай бұрын

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

@Max892-s 5 ай бұрын

Cool👍

@learncommunolizer 5 ай бұрын

Thank you very much!!

@Yureka-ox5jn 3 ай бұрын

Thanks❤

@xaviersoenen4460 7 ай бұрын

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

@rabotaakk-nw9nm 6 ай бұрын

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

@nagarajahshiremagalore226 3 ай бұрын

Sole : X cube - y cube = xy + 61

@user-gr1rf1rg5s Ай бұрын

- 528 no +528 attention

@SaiPraveen-ss8vj Ай бұрын

@TWJRPGGamming 8 ай бұрын

2,-2,2i,-2i

@tamarshahverdyan2723 2 ай бұрын

@Ginkobil50 4 ай бұрын

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

@gmeier391 6 ай бұрын

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.

@sankariraman6453 8 ай бұрын

What abt x=16or 81

@sankariraman6453 8 ай бұрын

No leave

@bonitokumar4977 6 ай бұрын

Olympiad time over .

@user-nd7th3hy4l 3 ай бұрын

X=16

@sonuok 4 ай бұрын

very time consuming. Sovle this intuitively guys.

@DonaldKim33 5 ай бұрын

When I asked Chatgpt, x is about 32.86.

@kienbui6262 8 ай бұрын

@user-yq2uf1si4c 8 ай бұрын

81=97-16

@user-lf1bm8fm2g 8 ай бұрын

Очень четкий и грамотный ответ. Браво-бровисимо.

@doowadiwadi 5 ай бұрын

Way too easy to be a Math Olympiad question.

@valeriyabakumov1652 6 ай бұрын

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

@user-dq3uh6ee5w 4 ай бұрын

16, 81.

@Lars_Porsenna 4 ай бұрын

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

@user-cw5ec9hk6lh 6 ай бұрын

X16

@user-nd7th3hy4l 6 ай бұрын

X=81

@dardoburgos3179 16 күн бұрын

X= 16. No hace falta explicación.

@pholdway5801 3 ай бұрын

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

@user-gh8gk3xo7u 5 ай бұрын

А теоремой Виетта у вас не пользуются?

@user-xc5os4ep3n 4 ай бұрын

Можно просто 5 возвести в четвертую степень

@CS-vm7lq Ай бұрын

Mi mente me dijo que el valor de X es 16

@user-vn6uc7ib6d 2 ай бұрын

Чому не використовуєте теорему Вієта?

@user-oe5nb1nh9c 4 ай бұрын

×=16

@oahuhawaii2141 4 ай бұрын

What about x = 81?

@olgaa8310 6 ай бұрын

Too complicated for my 73 yr old brain to comprehend

@yudithmanco9840 4 ай бұрын

Solo entiendo el español.

@khalifauduman5598 6 ай бұрын

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.

@user-qr7dw4hk6x 5 ай бұрын

Меньше десяти секунд на решение этоц олимпиадной задачи.

@user-lf1bm8fm2g 8 ай бұрын

Х=81 .

@heniwatisetiono6995 8 ай бұрын

x=16

@oahuhawaii2141 4 ай бұрын

What about x = 81?

@user-xs4rm1kh7f 8 ай бұрын

😂😂😂😂😂

@user-yi7ic4iu7f 8 ай бұрын

🎉🎉🎉😂😂

@user-pi2my7vk5j 3 ай бұрын

Много ненужных подробностей!При решении!

@user-nx9wy5sh9w 7 ай бұрын

太複雜了

@user-lf1bm8fm2g 8 ай бұрын

Африканец с аналитикой молодец.

@user-tu4mq8qx6i 4 ай бұрын

А почему a^4 + b^4 = 97?🙄🤔

@oahuhawaii2141 4 ай бұрын

a + b = 5

@miracbarsapaydn650 8 ай бұрын

X = {81,16}

@mariapiapiro3718 6 ай бұрын

Non è chiaro può spiegare in altro modo?

@SidneiMV 17 күн бұрын

∜(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