Ramanujan ने कैसे निकला इस Equation का Solution | √x+y=7 x+√y=11 Solution
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- Опубліковано 7 лют 2022
- An interesting problem posted by Srinivasa Ramanujan √x+y=7 x+√y=11.
Solution:
x + √y = 7 and √x + y = 11
Consider
√x + y = 11
√x = 11 - y
Squaring on both sides
x = 121 - 22y + y2
Put x = 121 - 22y + y2 in the equation x + √y = 7
Let √y = z
we get 121 + z4 - 22z2 + z = 7
We get factors z = ± 1, ± 2, ± 3, ± 6, ± 19, ± 57, ± 114
z = 3 satisfies the equation.
Now find the value of x and y we get x = 4 and y = 9
Srinivasa Ramanujan (1887-1920), the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including mathematical analysis, infinite series, continued fractions, number theory, and game theory is recognized as one of history's greatest mathematicians. Leaving this world at the youthful age of 32, Ramanujan made significant contributions to mathematics that only a few others could match in their lifetime. Surprisingly, he never received any formal mathematics training. Most of his mathematical discoveries were based only on intuition and were ultimately proven correct. With its humble and sometimes difficult start, his life story is just as fascinating as his incredible work. Every year, Ramanujan’s birth anniversary on December 22 is observed as National Mathematics Day.
Ramanujan’s major contributions to mathematics:
Ramanujan's contribution extends to mathematical fields such as complex analysis, number theory, infinite series, and continued fractions.
Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today. Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics.
Game theory: Ramanujan discovered a long list of new ideas for solving many challenging mathematical problems that have given great impetus to the development of game theory. His contribution to game theory is purely based on intuition and natural talent and is unmatched to this day.
Mock theta function: He elaborated on the mock theta function, a concept in the field of modular forms of mathematics.
Ramanujan number: 1729 is known as the Ramanujan number which is the sum of the cubes of two numbers 10 and 9.
Circle Method: Ramanujan, along with GH Hardy, invented the circle method which gave the first approximations of the partition of numbers beyond 200. This method contributed significantly to solving the notorious complex problems of the 20th century, such as Waring's conjecture and other additional questions.
Theta Function: Theta function is a special function of several complex variables. German mathematician Carl Gustav Jacob Jacobi invented several closely related theta functions known as Jacobi theta functions. Theta function was studied by extensively Ramanujan who came up with the Ramanujan theta function, that generalizes the form of Jacobi theta functions and also captures general properties. Ramanujan theta function is used to determine the critical dimensions in Bosonic string theory, superstring theory, and M-theory.
Other notable contributions by Ramanujan include hypergeometric series, the Riemann series, the elliptic integrals, the theory of divergent series, and the functional equations of the zeta function.
Ramanujan‘s achievements were all about elegance, depth, and surprise beautifully intertwined. Unfortunately, Ramanujan contracted a fatal illness in England in 1918. He convalesced there for more than a year and returned to India in 1919. His condition then worsened, and he died on 26 April 1920. One might expect that a dying man would stop working and await his fate. However, Ramanujan spent his last year producing some of his most profound mathematics.
#ramanujan #ramanujannumber #ramanujansolution #ramanujaninfinitesum #Ramanujanparadox
Scripted By: Ghatak Thakur
Voice Over By: Dheemraj
Music: Maestro Tlakelel
Artist: Jesse Gallagher
FAIR USE COPYRIGHT DISCLAIMER: This video is solely meant for educational purpose. We do not claim that all the information in this video is 100% correct some may be hypothetical.
Thank You...
I am so sorry guys i did mistakes at two points which by the way do not affect the solution of this problem😔
I have done very hard work in making this video so I can't re-upload it , I request you a to please understand the mistake and make make correct solution 🙏
Bhai iss msg ko pin krdo
@@aditya4438 hamhu ikra yahi bol rahe h
@@IITian_Shivamm Aree😅😅
@@aditya4438 😂
Bhai pin karo इससे
The Greatest mathematician of the world. Though he was born in a very poor family but rose on the top with his hard work and talent.
Personal 👆Game lene ke 👆liye WhatsApp karo👆..
No talent goddess help him
It can be more simplified :
*√x + y = 7*
from here we can get
*[ 7 = √1 + 6 or √4 + 5 or √9 + 4 ]*
Only *(√9 + 4)* is a pair of two perfect square numbers. So x = 9, y = 4
Aapka logical mind acha hai
Bilkul sahi. Aasan cheezo ko complicated nahi krna chahiye. Is video m wahi kar diya
Lekin aap ko solve karke dekhana hoga
How do you know that √9 + 4 is only pair You need to prove it mathematically
@@GauravGamer9 yes correct
Instead of the elaborate calculation, put p=√x and q=√y, to get p+q^2=7, p^2+q=11. Solving, the equations, we have, (p-q)(p+q-1)=4 and the first bracket will be equal to 1 and second 4. This is the only solution. Resubstituting, p,q, x=9 and y=4.
1st bracket ko 4 bhi le skte h or isme aap fs skte ho
Or tumne jo tarika laga h vo video wala hi h bs tumne (p-q)(p+q-1) ko direct likh diya h
If first bracket is 4, then p=q+4 and p+q-1=1 implies q is negative which is not possible
Sir ghoom gaya
@@ramanma9915 ha vhi to phle reply m likha h bhai
Ramanujan was such a profoundly brilliant mathematician. This video does not even begin to convey any of his astounding discoveries.
yes, because this video is not about Ramanujan, but solving a equation. Only mathematics lover or interested person would click on such videos
@@piyushdaigavhane3488 you're right, having his name and photo does not connect him at all bahahahahaha
ua-cam.com/video/d30zWsrIo0M/v-deo.html
i this he has a mistake in first equation
I thought it this way and got the solution as (4,9)
Firstly x, y have to to perfect square, as their sum gives integer, and should be less than 11, 11 because x and y are inside root, and root of negative is not possible, so x and y are positive and maximum sum we got was 11,
Then perfect squares below 11 are
1,4,9.
I substitute these in both equation and 4,9 satisfied the equation.
X=9and y=4 is ans u are wrong
What if it ranges to the big numbers 1000,10000000... Then what would you do?
wowww that's cool how you calculated it🤩... why haven't i thought about it.😅
Bahi easily ban gya bahut easy question pata nahi kaise kohi ise solve na kar paya
Same here ....we 2x speed ramanujan
इतनी मेहनत करने के बदले आसानी से ऐसी संख्या लेने हैं जिनके वर्ग मूल ज्ञात हों और छोटे हों तो बहुत आसानी से हल मिल गया। मैंने विडियो रोक कर हल पा लिया था।
The Great Ramanujan 🔥❤️
Great indian mathematician....
❣️❣️❣️❣️❣️❣️
Our great mathematician Ramanujan used to prayer to the Goddess namagiri by sitting in the centre of four pillar Mandap facing the Goddess in the Narasimha Swamy Temple. it is said that they stayed in the precincts of the temple for 3 days and event take place when Ramanujan got the permission of the Goddess to go to England in a dream when he was asleep another. By the blessing of devi he became a great scholar.
@@ug1880 has kyu Raha he be
Tum bhi aesa hi karo 😉
Personal👆 game lene ke liye👆 WhatsApp karo👆
You watched the movie
🤣🤣🤣🤣🤣
X=(7-y)^2.....(1)
Y=(11-x)^2......(2)
Then put possible values of y in eqn (1) and you will get y=4 satisfies both eqn
Personal 👆Game lene ke 👆liye WhatsApp karo👆..
Y=4
X=9
it's about algebraic solution ..there are lots of genius who got the answer by valye putting
I am trying this equation without watch this video since 5 days by different ways,but you believe me I didn't ❤️❤️❤️
Thank you for sharing such a lovely video
It is. Very simple to solve I have find it by easy method I found x=9
Y=4
Sahi bola
Tell me that method
Value putting method😆
I deduced one thing initially , x and y both need to be perfect positive squares.then used hit and trial starting with 1,4,9 as x values
If Sri ramanujan would have survived more years the he would have probably beat all the mathematicians we know upto now
In such a small duration of his life he had discovered such a huge number and theorems
Really a salute to such a genius 👏👏👏🙏🙏🙏
In india always born a great mathematician.
Mere teacher ne ise 10th me pdhaya tha.hamlogo ne ise substitution method se bnaya tha.
Ise bnane me bahut maza aaya tha
Other who have solved mcqs....
Will try through option only....😅
But ya this was great....😇
Bro the way you solved is somewhat similar solving to olympiads level question like you have assumed root x- y =2 and if it satisfies the equation then it can be the answer
beautiful style and solution of problem
done by hit and trial under 60 seconds..both need to be perfect squares
Mene toh isse Bina solve kiye , mann mai hi x and y ki value nikal Diya❤️
Try to change constant with 12478 and 14789 then say maine toh ase solve kr diya
Great... Mind blowing
Bhai Sahab Ye to bahut Simple Question tha ...Mene Dekhte hi Ans Mind me aagya tha 9 and 4
I got the answer in 10 seconds 😅
X and Y are either 4 or 9
Seeing the equations clearly the answer is X=9 Y=4
Galt hai
Same here 😂😂
Me too bro😅
Mee too😂
Wrong bro
Thanks for uploading this video
I solved this very easily and found the value of x and y without using pen paper or pencil
Me tooo
Tell me how
Please can upload the image of ans
Don't be over smart
Ramanujam k baap
In my whole life, I want to solve this equation by algebra, but no success,today I know that it is not possible but still i dont believed that it could be solved via algebra.
1st equation is clearly showing value of Y must be less than 9...and coz perfect square is needed so only 2 values can be used for Hit & Trial method i.e. 1 & 4...in case of 4 we are easily getting value of x as 9...and so it would hardly take a minute by hit and trial method
The method you used is not completely rigorous and there are some loopholes which are
1) if x and y are integers then it is not necessary √x-√y is an integer. It is possible that √x-√y is an irrational no and product of two irrational nos can be rational for eg 2√2*√2=4 so you should prove why u didn't consider this case.
2) In fact it can be proved that x and y are perfect squares as follows
Since √x=7-y so √x must be an integer which is only possible when x is a perfect square. Similarly y is a perfect square. So if we write x=a² and y=b² then we will use the argument you told to get x=9 and y=4.
The incompleteness in your proof is only that you didn't show x and y are perfect squares because then only u can say √x-√y is an integer otherwise not.
It's already metioned x,y € z and he also said x,y belongs positive integers
Think it's kcnag
Ye Bahut Easy Question Tha Bhai Intermediate Mein aise Bahut sare Sawaal Lagaye hai
🤞 itz 💯true method
There is nothing calculation mistake anywhere
I did same type of questions
(ab =somthing
a+b= somthing find a,b which belongs to integer)
But i never thought this is that type
math is ✨
Best video
Thanks Bhaiya🎯💪👌👏🙏
We can use inequality by which we x smaller than 11 and is a perfect square and is odd number
If one has to solve by trial and error then by observation it can observed it's solution within few second . And you have atlast used possible solutions !
Genius solutions..wah no words....jay ramanujan
Hello! What's a radical text font? Thanks!
4 and 9 bhai use trail and error method
Ekdam bindas😎😎
I think when you change it 1:11 then it should be_[ (y-x)-(-√x+√y)]🤔🤔
@asit mandal you are correct
Ha bhai Mai bhi
Let's drive wale bhaiya plz correct your this mistake
I just simply put the value and surprisingly it proved😉
I aso bro 😂 we r also very generous 👍😂
Same here
We can satisfy for 1st eqn 1,4
For 2nd eqn 1,4,9 bcz those are the only square from 1 to 10
Personal 👆Game lene ke 👆liye WhatsApp karo👆..
I solved it in just 1 minute by just thinking it
That was very easy 😊😊
give me the solution
Vishal Gautam me too 😊
great one
I have found values by hit and trial.
X = 9 . Y = 4
root x = 3 +
y = 4
X =9 and root y = 2
Yrr iss question ko meine bhahut phele hi solve rakha hai🌜✌🏻🌛 ,
I am literally not lying i swear I just calculated the values by seeing thumbnail and came to see video for the answer and I was right I calculate the answer by hit and trial and I swear it takes me less than a minute 😯
There is giving that x and y are integers so the y is the only perfect square because of root of y is integer then value of y should be less than 7, there is the two possibilities;y=1'y=4 in the equation y is equals to 1 is not satisfied so y =4 answers.....
He is great man
Super sir jii
Ramanujan is legend 😮😮
Very interesting information
2:23 this is hit trial
And after seeing the question eq.
I soved it in 15 sec. without reaching this stage itself
Listen bro in mathematics there is no transferring of -1 or 2 to other side of equality .it is just adding +1 both side or dividing by 2 both side .
Itna asan maths Puri duniya me bas ramanujan se bana mene toh turant banadiya
Substitution method is the simplest way to remove it. And I did resolve same way..so no need to drag the great Ramanujan
Thumbnail dekhke Yuhi socha 9 aur 4 just for assuming..but fit ho Gaya...wohi answer Nikla 😯
Excellent.
ua-cam.com/video/d30zWsrIo0M/v-deo.html
And how about equation at 1:45 changing to equation at 1:47 ???
It was +(x^1/2+y^1/2) and the next moment it's - (x^1/2-y^1/2) 🤔
🤔🤔
Which software do you use to make these videos
आज अगर महान गणितज्ञ रामानुजन जिंदा होते तो इस वीडियो को देखकर फिर से मर जाते
या फिर इस यूट्यूबर को ले जाते
Wah sach much maza aa gya
These equation are very easy
I solve this equation in just 5 second
by hidden trial method
X is equals to 9 and y is equals to 4
Very easy
We can easily find the values with graph it is damn easy
x = 9
y = 4
VERY EASY EQUATION FOR ME
VERY LENDI METHOD
Solved it in couple of mins with basic method of solving equation.. not sure why it’s so difficult
check 1to 9 which have sqrt
as1,4,9
now check which is satisfy both equetion
ans-x=9 y=4
then
But root x and root y can be negative also and integer values are accepted ..so it should be absolute of root x/y
X=9 y=4 these are complex no with irr part =0
Mann me hi krliya
Ik shayd is eq ke aur complex root ho skte hai
Bohoth Prasanna hei!
Just took 10 seconds, by applying substitution 😊
mathematics ka maan behen aik kardia . pehli dafa dekha values ke darmiyan comma he .
agar aise formule banaye jae to main 2000 ke bajae 10000 bana don
By making rough graph it can be calculated easily in few second as i did
Dude it was too easy. Even I didn't have to hold a pen 🖊️.
Awesome
Please upload any other method of solving the example
I got the answer of this equation when i saw your video thumbnail x=9,y=4
I was looking for generalized solution but this is again guess work at one point.
It could have been done at first place
(X,Y)=(9,4)
X= 9 and y= 4
Ramanujan :- uses 100% of brain to solve this
Legends :- bhai muze to dekhte hi pata chal gaya ki x=9 aur y=4 hai 😂
Bro you have to prove this
That is hit and trial method
Prove it logically
Bro maine bhi aise hi kiya and jo proove krne ko bol rhe h
Toh Ramanujan ji bhi keval theorem de dete the kuch theorem toh aisi bhi h jo abhi tak proove nhi hui h
Sir iski values sirf 7 aur 11 ke equal thodi hogi , aur baki numbers ke bhi equal ho sakti hai jaise 13 aur 19 ?? Jisme x =16 aayega and y=9
It's very easy..X=9,Y=4
Legend never die
1:44 se 1:50 me ye kaise hua. . . ?
(√x)² - (√y)² + (√x + √y) = 4
(√x+√y)(√x-√y) - (√x - √y) = 4
nichay minus kaise aa gaya ?
Yessssssss
Totally agree
Bhai saste nshe
Bhai bande ne comment Kiya h ki usse galti hui h
Ye bas video bnate h inhe nhi pata bechare simple and easy way ...
X=(7-y)^2.....(1)
Y=(11-x)^2......(2)
Then put possible values of y in eqn (1) and you will get y=4 satisfies both eqn
I tried and get answer 👍by value putting method.
I Think This approach
is wrong but the Answer
is correct x =9 & y=4
Try the same approach on the question below
x+y=6
x-y=2
( x + y ) - ( x - y ) = 4
square of root (x + y ) - square of root (x - y ) = 4
[ root (x+y) - root ( x-y ) ] . [ root (x+y) +root ( x - y ) ] = 4
Now Take -
root (x+y) - root (x-y) =2 eq ( I )
&
root (x+y) + root ( x -y ) =2 eq ( 2 )
solve it
root ( x + y) = 2
so x + y = 4 but in the question
x + y = 6
Very easy √16+ 3 for first equation and 8+√9
Bhai x and y ki value same honi chahiye
Your answer is correct
X=9, y=4 I have found the answer in 20 second
Put √x = p and √y =q...and substitute equation 1 in equation 2...we get a biquadratic equation..
X=9
Y=4
Brilliant
Maine hit n trial se x9 aur y4 nikala
Edit. Yes yess yesss 🔥 hit and trial se hi sai but mera answer sai hai
By hit and trial
In 5 seconds i got it
X=9 y=4
Correction occured in your solution. So find out and correct it.
X=9,Y=4
√X+Y=7
3+Y=7
Y=7-3
Y=4
Or, X+√Y=11
X+√4=11
X+2=11
X=11-2
X=9(prov.)
Good inteligent
√4+5=7
√9+8=11
Can this be done?
1.22 pr jo equation apne likhi h..Vo wrong likh di h...esliye jyadatar log confuse ho rhe h...Right Eqation
(X-Y) - ( Sq root of X - Sq root of Y) = 4 hogi.
Very easy class 10 mathematics question