Important Question Taken From Russian Math Olympiad | Finding Positive Integer | Aman Sir

[@yashsinha1509]

Sir when you calculated for a=2, you wrote 52/5 but it was 53/5. But it doesn't matter at the end as that too won't effect the answer. Thanks for such a beautiful solution 🙏👍

[@pkhisanjeevkumar2048]

Done in 60 sec by observing and manipulating ( x - y )(x2 +y2 + xy)=xy + 25 + 36

[@anuraggautam8710]

I also do this

[@atulyaroy8962]

Exactly

[@aviralkumarbarnwal83]

Sir plz aap Olympiad maths pr koi course laaiye plz khaaskar number theory aur geometry ke liye.Namaste aur video ke liye thanks

[@mathe-magics8451]

Hiii aviral I'm also a big fan of osho😌

[@monujhembrom9279]

Yess sir please

[@aviralkumarbarnwal83]

@@mathe-magics8451 Namaste bhai.Sunke bahut achchha laga.

[@mathe-magics8451]

@@aviralkumarbarnwal83 👍❣️

[@414theConstant]

Yes please

[@djh9502]

Sir ese hi gjb gjb questions leke aao bhut mja aata h solve krne me

[@djh9502]

@@English_shahriar1 ok sir

[@Kirtiraj_Deshmukh]

My approach was:- x³-y³=xy+61 (x-y)(x²+xy+y²)= xy+61 (x-y)(x²+y²)+xy(x-y) = xy+61 Now by comparing coefficient of xy from both sides, We have x-y=1 Therefore (x-y)(x²+y²)= 61 (y+1)²+ y² = 61 ( since x= y+1) Here we get quadratic in y and we get y = -6,5 so x = -5,6 And we only select positive integers hence y=5 and x= 6

[@rankgammee9319]

Great

[@amanagarwal6057]

No, You are Wrong. You can't compare the coefficients of XY because they are numerals ( symbols written for numbers) and can be added to 61 and (x-y)*(x2+y2).

[@050138]

Comparing coefficients lol 😂 wrong method but right answer

[@createyourownfuture5410]

​@@050138 It's a wrong method but in number theory it generally works out

[@050138]

@@createyourownfuture5410 no lol, 🤣🤣 it's not just a wrong method, it is a blunder.... It worked it in this problem purely due to luck! When you compare coefficients, they should be constants not variables, otherwise they won't be called coefficients.... Here OP says coefficient of xy on LHS id (x - y).... When variable is xy, how can it's coefficient also be in terms of x and y.... Please don't kill maths by supporting such blunders! 🤦😅

[@kalipadadas823]

Sir just thora assumption lagake kare to bhi ho sakta hai jaise (x-y)=1, (x^2+y^2)=61 aur solve karne pe (x+y)=11 aur phir solve karne pe x=6,y=5 a jata hai. Kuki ye ek competitive exam ka sawal hai to aise bhi solve kar sakte hai fast karne ke lie.

[@itsbikidey]

Time stamp ?

[@03abhadilipdas94]

I got the same answer through a different approach. Notice that x^3-y^3 and xy are expressions of different degree, the former being of degree 3 and the latter of degree 2. Therefore, it can be safely conjectured that the latter overtakes the former at some point. Thankfully it is easy to prove as well. Fix y and vary x( then vary y as you like). Notice that [(x+1)^3-y^3]-[x^3-y^3]> [(x+1)y-xy] for x>y hence the former increases quicker than the latter. Now just check like 4 cases, x=y+1,y+2,y+3,y+4. The first case will yield solutions and the fourth case will be the end of our check because it will end up resulting in no solutions even in the reals, which means x^3-y^3>xy+61 when x is greater than or equal to y+4

[@huh4157]

How could xy be of 2nd degree

[@03abhadilipdas94]

@@huh4157 what degree is it of then?

[@huh4157]

@@03abhadilipdas94 ahh sorry my bad. I misread it 😔

[@mathematician5785]

Sir, maine khud se kar diya Same tareeke se Thanks sir

[@paraskumarbabre4075]

I got this solution within 5 min ☺☺ But sir thanks for giving such beautiful question

[@arkapravachaudhuriix-e-11s26]

yet another approach: multiply by 27 on both sides to make (3x)^3+(-3y)^3+(-1)^3-27xy=1646. now the LHS is in the form of a^3+b^3+c^3-3abc which we can factorise and also we can factorise the RHS and by comparing the factors we get x=6, y=5.

[@TrulyAmazingChoices001]

bhai tune (-1) kaha se laya, 27 se multiply karenge toh (3x)^3 + -(3y)^3 _ 27xy = 1646 aayega!

[@sagnikghosh630]

Ekdam bhannat🔥♥️♥️

[@tridibdasgupta1754]

Bohut achchha upka teaching. style, very inspiring.

[@evillive-cv7wu]

for x in range(1000): for y in range(1000): if x*x*x - y*y*y == x*y + 61: print(f"The values of x and y are {x} and {y} respectively")

[@evillive-cv7wu]

Its logical that x and y can't be greater than 1000 in this case... So i randomly chosen 1000 and tried for all possible integer value from 0 to 999 as range(n) returns 0 to n-1. When the numbers from the loop satisfy the equation.. the result is printed using print function.. ah! Solved in just 6 sec... 😅 5 sec for writing one second for running it...

[@arushimishra]

You are the best Aman Sir ❤️. Thankyou for always motivating us and helping us making Mathematics our favourite subject . I've been weak in maths since class 10th. Then too I took pcm in 11th 😅 And saw your video on KZbin and that was the best thing happened to me ❤️ I start seeing maths as fun and I'm enjoying it ❤️ Thankyou so much sir ❤️

[@arushimishra]

@@Adityathakur.-_-_-_....984 sure

[@arushimishra]

@@Adityathakur.-_-_-_....984 dekho for chemistry you can prefer only ncert jee ke liye ekdm padh daalo subah ka ek routine bana lo ki ek ghanta organic padhna hai aur baaki ek ghanta tumhe uska question solve karna hai ..that will be helpful . Jo topic tumhara cover ho uska pehle ncert level karlo fir advance books solve karna . And for organic and physical you can also prefer alakh sir old yt videos he explained there very well . Baaki read ncert and practice questions daily

[@arushimishra]

@@Adityathakur.-_-_-_....984 okay sure

[@Khusi987]

Sab observation ka khel hai

[@raunakkumar9377]

@@Adityathakur.-_-_-_....984 *बेटा तेरी कलाकारी साफ नजर आ रही। बिना किसी को तू जाने उससे गाइडेंस कैसे ले सकता है वो भी एक स्टूडेंट ही है।* *That's why girls afraid to write anything in social platform because of people like you...they need freedom.* 🙏

[@GOURAVKUMAR-we5sk]

Sir bina aapke math me mjA hi nhi hai🥰

[@ARYANG.S.]

Sir Kasam se yeh question mind mein hi kr liya thank u sir

[@pkhisanjeevkumar2048]

Follow you and NV SIR from last 2 years

[@asadfoujdar207]

Thank you sir aap ese hi bhannat questions karaate rhiye hame guide karte rhiye...

[@asadfoujdar207]

@@English_shahriar1 have you any KZbin channel...

[@zhugzhuangzury]

Sir a similar type question is......... 2abc=a+b+c+4.Find all the non zero solutions of (a, b, c)

[@notananimenerd1333]

Ioqm camp ka question

[@zhugzhuangzury]

@@notananimenerd1333 Sorry which camp?

[@notananimenerd1333]

@@zhugzhuangzury oh sorry, actually this question was asked in ioqm camp run by vedantu for maths Olympiad

[@Meme.r7-y3g]

@@zhugzhuangzury i solved this in two step

[@ritupravaadhikari1727]

​@@Meme.r7-y3gmai bhi

[@ktgaming9496]

I solved it in 5 sec by hit and trial. X=6 y=5 you can put the value direct in Question by shifting xy to left side.

[@AdrenergicSquad]

I took 30 sec and half page

[@31.shambhurajraut92]

I took 2.30 min but I am in 7th . Preparing for prmo (next year) :)

[@ilezx]

@@English_shahriar1 bhag

[@radiobum986]

Sir the same question with changed constants came in IOQM for 2 marks

[@hskstudies2412]

Sir please IOQM ke lie bhi playlist laiye

[@kushalkambar5182]

Sir plz make videos on 10th competitive questions

[@fazlayscreations5801]

solved before seeing your video in 3 minutes! 🙂

[@narayanmodi11]

sir yeh kaun se class ka question hai plzz bataiye

[@programminghub8663]

Please bring course on pure maths olympiad

[@0-to-Hero-hub-hridanshsurana]

a = 2 mai b = 53/5 sir. 5:22

[@honestadministrator]

Interestingly at x= y +1 , y = 5 is a feasible solution. 6^3 - 5^3 - 5*6 = 61 Again (y+1)^3 - y^3 - y(y+1) = 1+ 2y(y+1) grows up with rise in y, therefore no feasible solution is possible for x= y +1, y > 5

[@mehulpunia6174]

Sir please make more videos on these type of questions

[@aayushsinghrajput402]

Sir my 12th me hu aur aapka class hamko bahut achchh lagta hai math ka 😘 so thanks sir ji

[@aayushsinghrajput402]

@@English_shahriar1 ok

[@adityaprushottam4873]

an easier method : x^3-y^3=xy+61 (x-y)(x^2+y^2+xy)=1.(61+xy) comparing corresponding quantities : x-y=1.......(i) ; x^2+y^2=61.......ii squaring and expanding (i) x^2 + y^2 -2xy=1 => 2xy=61-1=60 => xy=30 now , (x+y)^2=(x-y)^2+4xy taking root( as x,y>0 =>x+y >0) x+y=sqrt(1+ 4 . 30) =>x+y=sqrt(121)=11 .......(iii) now from (i) and (iii) x+y=11 x-y=1 -------------------------- on solving x=6,y=5 (x>y)

[@RaMta-joGi-pm2ct]

Sir what is Lambert w function

[@atharvasingh3596]

Same type of question was asked in ioqm(maths Olympiad) on 30th oct. (q 6) ,& thanks sir maine kar liye coz of u🔥🔥

[@RohitKumar-lw8th]

Love you sir ji 🔥🔥🔥❤️🔥❤️🔥❤️🔥 guruji 🔥❤️❤️🔥

[@subhadeepdas8938]

Sir pls reply biggest fann!!!

[@vishalvedi8922]

Nice sir

[@saisathwik7819]

NICEEEEEEEE QUESTION.....

[@debaprasadhalder7982]

Excellent solution

[@jatinshahu3562]

Sir please koi course launch kare

[@kushanraj1414]

Sir please make a video on SL Loney Coordinate Geometry book review

[@mathe-magics8451]

Gajab

[@sanjeevroy1436]

Thank you sir. Good question and solved. 🙏.

[@nasaXtalks_buds]

Hi sir your teaching method is very nice

[@chinmaychakrabarti7632]

Very logical solution

[@noname-jv6hx]

It was easy for a math olympiad question

[@Alphamatics1234]

Best explanation sir love you

[@rajendragupta9087]

Sir pls engineering mathematics ki class shuru kijiye

[@rajatsarkar4288]

Sir if positive integer solution is required then x³ - y³ -xy = 6³-5³ - 6.5 therefore x,y= 6,5 and 5,6

[@tahseenraza8601]

Sir plz make a lecture on Echelon form of matrix

[@harshitrana7157]

IOQM aspirants would love this

[@parth-the-artist]

My approach Know the formula x cube - ycube x^3-y^3 =(x-y)(x^2+y^2-xy) so we will try to find two squares whose sum is 61 so that fatoring will be easy they are 36 and 25 so numbers are 6 and 5 (x-y)(x^2+xy+y^2)=5^2+61+6^2 we can see that x-y has to be 1 so we reject x=5 y=6 as it will give -1 solution is x=6 y=5 I know this is not very mathematically/ methodically correct method but that's what I would have done if it were mcq exams like jee

[@mokshjain7403]

sir ji video mast thi

[@sha0305]

Sir mene voh 61+xy=x2+xy+y2 ko equal Kiya aur integer x-y=1 put kiya

[@ritik_A.I]

Sir pls cordinate geometry advance series Laurance confidence NHi aata

[@its24sahil]

Aman Sir Please Start One Shot Rivision Series for Class 11th and 12th Jee Students # Each chapter ka one shot 2-3 hour ka # Important question # Important Concepts # Important Formulas Please Launch Hurry Now Sir From 1st chapter of 11th maths to last chapter of Class 12th Maths I am waiting Sir for Your Awesome One shot Series

[@archit7890]

Mujhe bhi thoda bhut similar questions meri maths mam n revision m diya tha aur m class 9 m hu

[@ritupravaadhikari1727]

Bohot maja ata hai jab apne attempt karne keliye kebal 5 secs dete hai

[@gidskdsfjiafjifdifjdif]

sir we can also use the odd even concept here u taught ? ie interger = 2 types 1) odd 2) even putting every where odd therefore x^3 = odd y^3 =odd odd plus minus odd = even this on LHS on rhs odd * odd =even even + 61(odd) = odd therefore total this side = odd therefore LHS =RHS therfore 1 interger is there that will satisfy the eq. secondly if we put even now x^3 = even y^3 =even even + minus even = even this is LHS and even *even = even + 61(odd) = odd therfore LHS is not equal to RHS here therefore this cannot be the possibility therefore only 1 value will be there that will satisfy and now if we mentally put or by tukka or by chance we put 6 and 5 we get that too i think this might be smallest method possible for this question correct me if i am wrong

[@atanuroy3548]

Answer विल बी एक्स इज इक्वल टू सिक्स एंड y ईस कल 5.❤ 6:01 😅

[@NIRAjKUMARबिहार]

Aapka Each question mughee Kuch kuch hota hain wala song yaad aa jata hain sir Very nice (Niraj from Bhagalpur Bihar)

[@NIRAjKUMARबिहार]

@@English_shahriar1 @JUNIORMATHSBYNIRAJ My KZbin Channel I am teachers sir

[@shubhamrao7880]

Sir Real Analysis kya hota hai?

[@prakharverma7115]

Waaoo sir you are the best

[@seelamraviprakash3667]

Very nice Aman sir

[@amritsagarkar7899]

(x-y)(x²+y²+xy)=61+xy Compare both side. x-y=1. x²+y²=61 Solve both

[@Kirtiraj_Deshmukh]

Did the same way!!!!

[@rajeshdhaniya1642]

Nice

[@dictatorakshay369]

5:09 sir 52 nahi 53/5 aaega

[@khushitiwari8647]

Great teacher ❤️❤️

[@RohitKumar-lw8th]

Thank you sir ji 🌺🌺🥰🥰

[@rampassi1577]

Integers are always positive.fraction and neg are notintegers.Bhannat sir can you give more explanation for integers ?

[@Sunshine9p]

No dear, you are wrong. its not necessary that integers are always positive. integers comprise of natural numbers, negative numbers and zero. They do not include irrational numbers and fractions. I hope this would be sufficient but if not you can look 6th grade integers for more details

[@_Akash__Yadav]

Good night sir

[@TSAR-Vladimir_Putin]

sir ji CAT me bhi aate hai y

[@shubhisingh3339]

Sir we know that x-y is integer and 61 is a prime no. So nothing can be common in xy and 61 so x-y=1 and there we get xy=30 then solve it easily is this solution correct??

[@ankitavenue3590]

X=6 and y=5

[@dhruvitasoni3658]

Maja aaya🔥🔥

[@a2iconfacts658]

Sir apne 5 min se 5min 10sec mea ye bola ki 61-8=52 jo ki rong hai 61-8=53

[@sciencemathsmusic4067]

Sir all the things are fine but 😅 ... 2cubed = 8 and so 61 - 8 = 53 and not 52 ,.... Kindly consider that. Still, You are one of the best

[@shrikrishnagokhale3557]

Good

[@bsbrawl1653]

Sir I took 2 minutes and here's how I did it: x³-y³=xy+61 (x-y)(x²+y²+xy)=61+xy Now I assumed that x-y=1 and x²+y²+xy=61+xy and then substituted the values to get 5 and 6

[@Arandombharatiya-rt5kp]

Bhai how to increase thinking like this

[@bsbrawl1653]

@@Arandombharatiya-rt5kp bhai you just have to practice the questions like this from sources like JEE PYQ's , IOQM questions and all that stuff

[@flappy2903]

I actually got the right answer but I think my approach might be wrong. Pls rectify it ! It would mean a lot to me . Here's how I got it:- x^3- y^3 = xy + 61 Now adding x^2 + y^2 to both sides. We get:- (x^2 + y^2) +( x^3-y^3) = xy + x^2 + y^2 + 61. Since x2+y^2 + xy =( x^3-y^3)/(x-y) Substituting it there So we get (x^2+ y^2)+ (x^3- y^3)= [(x^3-y^3)/(x-y) ] + 61 Now since 61 is a prime number and also positive. We are certain that x^2+y^2 will be positive. So x^2+y^2 = 61 . On comparing the lhs and RHS. Similarly x^3-y^3 =( x^3-y^3)/(x-y) That means x-y = 1 Now we get two equations x^2 + y^2 = 61 x-y = 1 On solving we get x= 6 and y = 5. I might be wrong. Pls rectify my mistake.

[@orangesite7625]

Jab mei deka (x-y)(x²+y²+xy) = (xy+61) meje yad aya 61 yek special number hei aur x²+y² ka value 61 hona jaruri hei aur mei ne test kiya first with 7²

[@profabhishekiitr569]

Great

[@softtechplus383]

Easy question

[@mithileshbharti8281]

Sir solve this problem if x^y=y^x and 3x=4y then find the value of x

[@mithileshbharti8281]

Please

[@chandanrajputana2244]

X=6 Y=5

[@chaitanyapandey9323]

Value put 💪😎

[@swaryan1690]

x=6 y=5 is also a solution. Put these values and verify it yourself.

[@Angeltrisha2344]

Similar Qn in IOQM 2022

[@prakharverma7115]

Plz start jee advance session

[@saurabhsinghal102]

When a =2, b should be 53/5 and not 52/5. Eventhough it does not matter 🙏

[@anupamdubey5335]

Ha ha same bro

[@eklavyasingh8143]

Maths is just like life , one can simplify it by simply observing some simple things

[@imsomeone_really_insignifi6634]

Compare karke x-y=1 Nehi likh sakte?

[@imsomeone_really_insignifi6634]

@@English_shahriar1 Ok

[@classxteaching..4067]

Sir bsc course le kor ayo

[@shashankkatiha9439]

x^3 - y^3 = xy + 61can be written as (x-y)(x^2 + xy + y^2) = xy + 61 or (x-y)(x^2 + xy + y^2) = 1.(xy + 61),this means x-y =1 and x^2 + y^2 =61. Solve these two to get the solutions as (6,5) and (-5,-6). The latter can be ruled out as per the given condition to give(6,5).Now I'm writing this before watching the video. Don't know what his solution would be..

[@MuditJhawar]

I expanded the equation and got x,y = 6,5 from hit and trial in a minute

[@sirak_s_nt]

It was merely your good luck.. as the question was pretty straight forward and gave only one solution, if it were to give multiple solutions, that too big numbers, your technique will fail People forget that anyone can solve few problems by hit & trail upto a mere extent, however, such people fail to develop any mathematical skills, and face difficulties in exam without options (integer type)

[@ravikantkumar7508]

Sir me to bin pen chalaye solve kar diya

[@alokraj2633]

At a 3 b value wrong

[@soubhikgorain]

Want your JEE ADVANCED series for maths pls if you want to launch the course then also pls sir make.... at an affordable price of 1000-2000. Everybody who wants pls show your support!!!!

[@mokshjain7403]

sir 61-8 52 nahi 53 hota hai

[@teamofeverything3128]

khudse kr lia sir 😀😀😀😀😀

[@hoodaharsh95]

🙏🙏🙏 Jii