China | Math Olympiad | A Nice Algebra Problem 👇
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I have a easier way to do this without the boring caculation part.
We first definite algebra A as 11111 and swap the big number in square root with algebra A
√(4444488889)=√(4A x 10^5)+8A+1=√4Ax(9A+1)+8A+1=√36A^2+12A+1=√(6A+1)^2=6A+1=66667
Yes the question 4s 8s and 9 makes us think in (A+B)^2 logic 👍🏽
Just use Newton iteration f(x) =x^2-a gives next x = (x^2+a)/2x. Start wit x = 67000 and after one iteration you are spot on 66667. Doesn’t take 3 minutes!
Pourquoi commencez vous par 67000?
D'où provient cette valeur ou comment la déterminez vous?
@@6bq7aez80 Maybe because the given number has 10 digits so square root has D / 2 digigts. 10^a^b = 10^(a*b). 67^2 and 66^2 is closest to 4444, 4489 and 4356 respectively.
@@Devishhikemerci. Je dois avouer que je ne connais pas par cœur les carrés des nombres bien au delà de 16 et je n'aurais pas pu trouver en moins de 3 minutes.
@@6bq7aez80 It's all about evaluation. For instance, 3600 is 60^2, so u may start Newton method with 60. Ok, even though you know that 4^2 is 16 then u can go on with 5^2 is 25, 6^2 is 36 and 7^2 is 49, so our result begins with 6 because the first 2 digits is 44 and the nearest value which is lower and is a square is 36. There is a manual square root algorithm with pen and paper (which does the same process I've described) u can look for it.
@@Devishhike la dernière racine que j'ai arrachée n'était pas carrée et re-apprendre à extraire une carrée m'aurait pris déjà les 3 minutes.
3mn vous sont une éternité mais pour moi un clin d'oeil.
Merci d'avoir satisfait ma curiosité .
Nice solution
Very well explained such complex question
amazingly stupid solution
Nice problem and excellent solution.👍
But you have to work on your 8's... 😉
Bravo, merci beaucoup.
Good food for thought. Thank you
Love the way you taught. It's a good example to solve a big question by using basic algebra. Thank you so much.
Just fantastic
Mast hey ye video
जुगाड करने की कला ही गणित कहलाती है,
Very, very good... I am impressed
x=11111,10^5=9x+1:
4444488888+1=4x*10^5+8x+1=4x(9x+1)+8x+1=36x^2+12x+1=(6x+1)^2
It's easier to just do the square root using written calculations.
a reasonable solution but difficult to repeat without seeing this method
AMAZINGLY STUPID SOLUTION, just let X=11111, 10^5=9x+1
Nice simplified
amazingly stupid solution
its very good simplified
Do we need to solve these problems to become rich? My boss stopped studying when he was 10 and now he has 10 Million dollards 😂
that's great😄😄😄
The mutual strikethrough of the square root and the degree of the number inspired me incredibly. It is possible that this should be done in the rice fields of a Chinese village... In our fifth grade, a schoolboy would be sent for his parents to find out how mentally complete this schoolboy is. But even for a schoolboy of an average rural Chinese school, the square root is actually a two-digit function. However, it is possible that China has a different algebra... I fell into prostration from the level of teaching algebra in China.
Too long for practice life, only for knowlodge. Is very very good
Nice explanation mam
Very well 😊
great😊
simple division process can do it in 2 mins why to do so much but process was good
Amazing
👍👍👍
Deep knowledge
also -66667 is another solution
wrong
ONLY 66667
Yes you’re done
@@leealex3692it’s not wrong
Only one solution! You're not solving an equation x² = .....
Result of squareroot is positive. Unless theres an imaginary number
Perfect learning
AMAZINGLY STUPID SOLUTION, just let X=11111, 10^5=9x+1
very interesting
Lose a mark for no negative root.
There mistake in second line
Lot of time you can find by division method quickly
直式開方更容易
嘿，你有學到直式開根號，不錯。
너무 반짝반짝 눈이 부셔 노노노노노
너무 깜짝깜짝 놀란 나는 오오오오오
너무 짜릿짜릿 몸이 떨려 지지지지지
오 젖은 눈빛 오 예
오 좋은 향기 오 예예예
Why not the conventional method that may take shorter time?
❤❤❤❤
(x ➖ 3x+2).
2^2^2^2^2^2^2^2^2^2^2^32^3^2^32^3^3^2 1^1^1^1^1^1^1^1^1^11^1^1^1^1^1^2^13^1 23 (x ➖ 3x+2) .
one two tree four five 🗣
Your process make your head dizzy.
You should using CAS to solve it.
Mathematic is learning, the scientist making calculator and computer, why you doubt them ?
You better at cooking masala.
It gave me slap on what I lost doing and thinking when i was a child
Столько лишних действий, глупых и не нужных, похоже чтоб тайминг растянуть, мне бы за такое решение 3 поставили.
And minus of the solution you found also will be another solution. Plus-minus
Thời đại 4.0 lấy máy tính bấm chưa đến 1 giây ! Làm dài dòng quá !
Mucho más corto calculando la raíz cuadrada a mano
この発想は無かったー！
did it wo paper in less than 30 secs
Try log
У стовпчик - куди скоріше.
99999 is not "five times nine"...
Красивое решение!
做的很努力，但冗長複雜，效率不佳，直式開根號可直接算出。
scam
Τόσος υπολογισμός για το τίποτα. Σε τι χρειάζεται;
Υπάρχει απλή μέθοδος, το κομπιούτερ
There is another way easier..
66667
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