Can You Solve This Problem From 𝗝𝗘𝗘 𝗠𝗮𝗶𝗻 𝟮𝟬𝟮𝟰, 𝟮𝟵𝘁𝗵 𝗝𝗮𝗻 - 𝗦𝗵𝗶𝗳𝘁 𝟮
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- čas přidán 31. 01. 2024
- Can you Solve This Problem ? 𝗝𝗘𝗘 𝗠𝗮𝗶𝗻 𝟮𝟬𝟮𝟰 - 𝟮𝟵𝘁𝗵 𝗝𝗮𝗻 - 𝗦𝗵𝗶𝗳𝘁 𝟮
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Kya solution h 🥶🥵
My respect for aman malik sir 📈📈📈📈
Bhai ye common problem hai
Yeh amazing soln nhi hai
There are better methods
tum ek method bata do
@@pratyakshYT95.5
@@pratyakshYT95.5 btao better method...mujhe to ye wala mast laga
in my paper i figured out the solution x=45 y=1 by hit and trial as 45 square was nearest to 2023 but i was not sure that it was the only solution so i left the question , great analysis by you sir
Mene bhi same yahi hit Kia but 30 seconds me hi question skip karke aage badh gya tha
Mujhe toh yaad hi nhi aisa koi question tha paper mein? Meri bhi same shift thi
I think udhar x and y belongs to n nhi tha
Aur isliye ek aur possible case bnega -45 wala
question different tha kuch complex numbers se related tha jitna yaad hai
🛐🛐🛐🛐
What a mind blowing solution!
This channel is very underrated...
rhne bhi do 2026 tk ☠
Aman sir, aapne aise solutions le aate ho saamne ki dekh kr maza aa jaata hai, aap jaisa teacher maine shayad hi dekha hai
x=45, y=1 (by hit and trial).
Frrr same i did
NAH, IF it's mcq then only it can happen
@@aayushjawalekar4169 Why would it not work lmao it's literally an answer and if it's wrong then the question can't be right
@@aayushjawalekar4169 No bro, if you can explain the analytical reason for your approach by hit and trial in subjective paper then also it's acceptable 😊
Kya solution hai sir🔥🔥😯 ekdum bhannat🔥🔥
I always love the solution when there is no loss of generality. Great solution sir.
Take modulo 4 assuming y>1 since x^2=-1 not possible since squares are either 0 or 1 mod 4 now this implies y=0 or 1,so you get the answer
PS:This only works since x and y are naturals
What a way of solving this, since I'm in my graduation but still I like to solve these JEE sums. Great explanation sir.
wow what a problem solving, so helpful to know the actual way to solve now i can use these ideas in other different situations too , thank you ! sir!
Brilliant problem and a nice solution strategy
this question don't demand any concept from any chapter of the syllabus just pure common sense, indeed a good question
It was a basic level olympiad question from prmo diophantine equation
@@thevibetree1 Seriously
@@KUMAR_ALOK_JEE2024kbhi olympiads nhi diya hai kya? 11th jee se tough maths 9th ioqm wagera me hota hai
Mathematics is a language of God ❤😊
What an analysis ... really fantastic.. Great Aman ji
Sir I tried another method, if we make this equation like this: 2^y+2-2+2023 = x²
=>2(2^(y-1) - 1)+2025=x²
Now x will be:
=> √2(2^(y-1) - 1)+2025
So now as 2025 is a perfect square and its clearly visible that making y=1 will make the value 2(2^(y-1) - 1) =0 hence we can say x=45 and y=1
Thanks sir👍
Nicee
🤌✨✨❤
This solution only proves y=1 is a solution. It does not prove that y=1 is the only solution.
It's giving u single value for it; But not a complete proof!
Same ways I solved it😊.
The very instant I saw 2023 and x², I rewrote it as 2025-2 because 2025 is 45², rearranged it as (x-45)(x+45) = 2(2^(y-1) -1). Rest is just deducing lhs and rhs as even or odd
MATHS IS NOT A SUBJECT IT IS FEELING
Ha bhai mera bhi favourite subject hai
❤❤
Yeah it is the best feeling in the world 🤤
My favourite subjects are maths and physics ❤❤❤❤
It's love bro
Sir , I have done it in a simpler way 😅
X² = 2^y + 2023
X² - 2^y = 2023
X² - 2^y = 2025 - 2
X² - 2^y = 45² -2¹
On comparing
X = 45 , y = 1
X+y = 45+1 = 46
Yes ,but you can't be sure if there are any other solutions
Matlab kuch bhi they are not complex no. 😂😂
@@AdarshShukla-le4gctoh usne complex number kaha use kiya?
Ye toh issliye kyuki you knew (45)² is 2025, othw it's just another guessing method
@@AdarshShukla-le4gc every real no. is complex no.
Sir I want to conclude one thing that you are a person from different planet.❤
Thank you Sir for this amazing question
Nice approach sir 😊
Loved this approach sir😊😊
Sir aap great ho kasam se itna accha explanation kisi ka nahi dekha hoga maine
I solved this in my mind in 5 seconds, u see there is a trick for perfect squares of numbers with unit digit having 5 , so 5² =25, 15² = 1×2 ,25 = 225 (we are doing 1×2 since ten's place is occupied by 1 and then we multiplt it by successive number) , 25² = 2×3,25 =625 , 35² = 3×4,25=1225 , 45² = 4×5,25 = 2025 , there we go we got 2025 now in lhs , 2ⁿ + 2023 we need to find the value of the power of 2 to make it 2025 if u look carefully the power should be 1 to make it 2023+2=2025 , now x is 45 ,y is 1 therefore x+y= 46 simple and very easy no need to waste 6 minutes lol
Yes bro 😂😂😂same thinking.What a coincidence.Class 9th mind same
Us Bhai Us
Agar subjective me ata to?
@@Wanderer-dd4mj it will never come , there's no chapter which has these types of question in ncert. Ncert is either too childish , or too hard
Ong same bhai
super solution sir great thought 🔥🔥🔥
Ye jitne bhi log tukka laga rahe hai.. Unke liye
615 + x²= 2^y. (x, y are non zero integers /can be both negative or positive) Find maximum value of x+y. Lagao isme tukka
ban gaya cool?
@@bruhyou197 mere se toh bana hi hua tabhi toh diya h 😅
@AkshunChauhan-bt6ey x, y = (59, 12) & (-59, 12) so maximum sum is 71, minimum sum is -47
@@sirak_s_nt bro us ques me max nahi pucha to possibility hai ki ya to ek solution hai ya fir agar kai solution hoge to unka sum same hona padega so hit and trial is best way in that question
@@user-go2rc5jo9ua/c to situation
Felt in love with maths again sir. Koti koti naman Aman sir❤
Best explanation sir...
sir acche se samjh aa gaya thank you so much
This question also came in my mock test yesterday....
Thank you sir for an outstanding explanation ❤
🤯🤯🤯🤯🤯 mind blowing sol.
This is why i tell to my freinds that you are the one who is giving me ideas.
Use both side log you can see directly
@@SKYLORD6905please provide solution using log
@@SKYLORD6905 Log 2023?
@@mukul9221 no use x²-2023 then take log then use log property tumhe kuch gadbad dikhheji kyuki ayega log(ײ-2025) ayega agr x=45 dal doge toh log define hi nhi hoga
Sir simple agar ham mod 4 kare to we know that every perfect square is 0,1 mod 4 and if we claim that y>2 then 2^y would be 0 mod 4 and 2023 is 3 mod 4 which is not possible and hence y
Exactly, simple ioqm examples lol
which chapter is it from? number theory?
Great ❤❤❤
This question is so amazing. Solving it with this method is even more amazing
Sir bahut aacha laga sir
What a great solution sir....
Mera shift
Ques me summation of all possible x and y puchatha. Thank you sir legendary soln...
29th shift 2 me tha yeh?
@@utkarshpandey01 yess
@@soumabhopal9901 kon sa question tha
Yaha par x, y € N tha ya R
Kyunki R mein toh ans 2 ho jayega
Masterpiece ❤
Wonderful solution sir😊
Truly great teacher and very well explained
What a beautiful solution sir and the beauty of maths damnnn !!!!
What a great thinking....maza hi aa gya...tukke se to Mera bhi ho gya..par te analysis dekh ke dil khush ho gya....
Sir isko graph se bhi to kar skte hai
Gave JEE in 2011 but man what a solution to this beautiful question. Just randomly youtube recommended me your video
Kya baat h sir salute h aapko
Sir very good explaination. Really enjoyed it.
sir i get many learnings about maths by watching your videos ,thankyou so much
jala dala bhai 🔥🔥
Maine 2023 ke sabse pass wala square dekha jo hota hai 2025 square of 45 toh isko x ki jgh rakha aur 2025-2023 kiya
Fir 2 bacha lhs me aur rhs me 2^y bacha equate krke y =1 aygya aur x = 45 phle se liya tha hence x+y = 46
Sir ye shi solution hai ?
you are too... good
Sir, procedure kaise pata kare. I mean how to know from where and how to start to solve a question
Yeh bahut aasan problem hai. Aur Aman sir ka soln koi bahut khatarnaaak nhi hai. Any IOQM student will nail it faster.
but in student should you following approch
1) x,y both are natural numbers
2) find perfect squares near 2023 which is 2025 so y=1 and x=45.
What a solution sir,you are best, salute 🫡🫡 to you sir.
Sir if we use trial and error method we can easily find the answer, it is very easy question for the 7th and 8th class students who knows the concept of squares and square roots.
Bhai Saab, kya solution hai. Sahi hai!
Sir 45 ka square 2025 hota hai.
Agar hum x ki jagah 45 rakhe aur aur y ki jagah 1 tho dono barabar ho jaenge
Answer - 45+1 = 46
😅 Hit and trial se kiya
Just beautiful sir❤
Great 👍 sir
This is also called solution by parity. Olympiads preparers would have found this extremely easy
Sir jee advance maths ke liye book suggest Karo please jaldi. Jisme mains ke questions na ho
jo log IOQM ki thodi bhi taiyari kiye hey unke liye bahut hi jyada asaan tha
Pata nahi jee coaching Wale number theory kyon nahi padhate
Diophantine eqn. Right
@@prashant34049 star batches me number theory ke basics padhate h and geometry me RMO ke pyq and Pathfinder krwate..
@@prashant34049 mostly nobody teach
Bhai tune kiya kaise diophantine se
Kidhar kagaya modulo
Elsborate krega mera to aa hi nai rha
@@monujhembrom9279
Fantastic analysis sir
Thank you sir
AMAZING EXPLANATION SIR 💗💗💗
This solution was just amazing like mannnn❤
🛐🛐🛐🛐🛐🛐❤❤❤❤❤ MIND blowing🎉🎉🎉
Will there be multiple integer solution of x and y. Or it is the unique solution.
Sir thank you so much for this solutions. Sir do you have any guidance regarding maths for class 9 students? How to practice such hard questions?
Chill kr be abhi ...11vi me ache se li jayegi sbki😂
First when i saw this qiestion i took the values of perfect square greater that 2023 which is 2025 =45²
i.e x=45 and y=1
Normal Application of Number Theory in Math Olympiad(Divisibility Theory)
Sir, Apne aisa samjhaya ki mai class 9th ka student isko samajh gaya.
sir yaha mene kya socha ki x2 jo hai jo vo ek odd number hai toa jo unit place hoga ex ka vaha odd number he ho sakte hai thn mene equation ko x2- 2023 = 2^y karke log base 2 leliya vaha se x2>2023 hona chahiye aisa aaya jisse ki ye patcha chal gaya ki xsquare ki value 45 hoyegi and vaha se y sidhe aagaya
love you bhai!
This was a perfect art!❤
Guruji tusi great ho
Thanks
Superb solution Sir , wahh Sir wahh ❤👌🏻
Though I'm in 9th class, this question felt too easy. I just first tried to find square root of 2023 which was around 44 and after that we have to add a factor of 2 to make it a perfect square and square of 45 is 2025 which is 2023+2 so y = 1 and x = 45 and as it is given that y and x both are natural numbers so no ±45=x. Therefore, x+y = 45+1 =46
for real this was more of a logical one
Sir easiest solution ye hoga ki y cannot be greater than 2 kyunki phir RHS (4k +3) ke form ka ho jayega jo kabhi bhi perfect squae ni ho skta so y=1 aur x =45
sir mere paas ek short trick hai☺. Aap pehele powers ko compare karlo jisse aapko 2=y+1 mil jaega aur aap further directly 2 second me solve kar sakte ho☺
thanks sir
Ye to sabse basic question hai hit and trial se hogya
Really ye sachme aya tha mains me
Sidhe y=1 rakhoge to 2025 kiska square hai 45 ka x=45 hogya
Dono natural number hai khtm😂😂
Ha ye ese question hote h ki dekh ke phli bari me click kra toh ho gya
... Vrna exam pressure me Kbhi kbar soch ni pate
Are you actually that dumb
What jf more pairs of x and y could exist
Clearly you do not have the iq level to solve this in the exam room
Question had asked all the possible pairs of x and y
Everyone could only predict a single possibility of y=1 and x=45
What if there were more
You cant take risks
Matrix Wale ka kya tha ans ......
@@vanshgupta6454 tumhara shift konsa tha aur exactly kya question tha wo batao fir ans bata dunga Mera 27shift 2 tha
Haa isse ho jata hai aise competitive setting mein
But it doesn't hurt to know the full beauty of the question
Sir aapse question poochna ho toh kaha pooch skte h ?
sir what about complex solutions? how many solutions will there be if x and y are not restricted to any domain?
But x,y are natural numbers as given in question, So it can have some decimal parts also and your assumption that either even or odd may fail ?
First I want to answer before seeing solution if we put y=1 then rhs become 2025 which is sq of 45 so x=45 then
X+y= 46
It hit me when I was looking at squares ending with 25 which are generally of numbers ending with 5
Sir and others fellow students pls verify
Nice concept
sir maja aa gaya iss question mei tho.
Pranam Charan sparsh peri pagdi apke pairo me
Kuchh v likhu Kam hai gr8 teacher
thank you sir.
X= 45 and Y = 1
Hit and trial...
Better for ioqm beginner question
Its a very very easy question, but maybe not in the exam!!!
Mind blowing solution ❤
Thank you sir ❤❤
Ok that's correct for this question because there is given x is a natural no. But u can't say even * even is div. By 4 or not even 2 because remember 0 is also an even no. That can cause confusion in another questions where it is not given ... Noone noticed it hoping it to be noticed by someone and this confusion should be clear so that maths can be bhannat ❤
but you can see that x will be an odd number as 2^y will be an even and by adding it with 2023 will result in odd .
0 is divisible by every number
Sir bina expand kiya bina kuch solve kiya pata chal jata hai x odd hai because vo equal hai hai odd plus even
One Liner, if y>2 then mod 8 gives x^2=-1(mod 8), which gives no solution to x. Then only possible values are 0
Congruence modulo is not in jee syllabus -_-. But number theory can be also used .
@@user-xq6ol2un7z I am sad that congruence modulo is no longer in number theory. - _ -. Jokes apart, I think you can try by divisibility of 8 ignoring modulos, provided even sufficient amount of time is there to develop the concept of modulo, by ourselves in exam hall. Lol😂😂😂
areee waah what a beautiful question dil jeet gaya
Respect from heart
Can anyone tell by putting value it is correct or not 🚫?
Awesome.