Students In China Had To Solve This Before International Olympiad

[@prithavirajsingh6937]

Ek Arsa beet Gaya lekin Aman sir Aaj bhi best hi hai❤❤❤😊😊😊😊😊😊

[@malasingha7099]

Sir, I have another solution of this problem but I don't know whether it is correct or not. However it is as follows Given that a+b+c=0. and we have to find the value of ( b-c/a +c-a/b +a-b/c)(a/b-c +b/c-a +c/a-b) Let b-c/a =x c-a/b=y a-b/c=z From above we get b-c=ax......(1) c-a=by.....(2) a-b=cz......(3) Adding 1,2&3 we get ax+by+cz=0........(4) It's already given that a+b+c=0.....(5) From eq.4&5 we can assume that x=y=z=1 Now replacing b-c/a, c-a/b & a-b/c by x, y & z we get the expression in the question as (x+y+z)( 1/x + 1/y + 1/z) =(1+1+1)(1/1+1/1+1/1) as x,y,z is 1 =3×3 =9

[@TT-ce7cx]

nice one bro

[@kindafool4083]

I think it's wrong.. its correct to prove that x=y=z however you can't say they are equal to one. They can be any number.

[@Therapoetic]

@@kindafool4083yeah but u can do 3x*3/x=9 n the method works

[@kindafool4083]

@@Therapoetic right, yeah

[@tentenben1085]

Wrong imagine if x was 1 it means b-a=c

[@aarushpaul3584]

My most favourite maths teacher on KZbin. Lots and lots of thanks sir ❤❤😊

[@AnjaliYadav-xg2no]

sir i solved it in first attempt and it was a nice experience keep bringing such question

[@zeroplays9915]

i did it using trignometry, a=tan(x), b=tan(y), c=tan(z) and assuming x+y+z=180deg, so [tan(x)][tan(y)][tan(z)] = tan(x)tan(y)tan(z) and tan(x/2)tan(y/2) + tan(y/2)tan(z/2) + tan(z/2)tan(x/2) = 1 and just put in a b c in the equation in form of tan and got the answer.

[@Manaschoudhary3636]

​@@zeroplays9915it is mentioned in Sl loney

[@dheeraj_dhakre]

The satisfaction you well when you solve the question in your first try.. Is unmatchable❤.. 🙃

[@skullgaming4977]

Sir I got the answer by multiplying both the brackets then simplifying two terms of them and six were identical terms so just wrote down same for other 4 and the remaining term was +3 and I got 9 by simplifying all the terms. Maza aa gaya sir... 😀

[@zeroplays9915]

i did it using trignometry, a=tan(x), b=tan(y), c=tan(z) and assuming x+y+z=180deg, so [tan(x)][tan(y)][tan(z)] = tan(x)tan(y)tan(z) and tan(x/2)tan(y/2) + tan(y/2)tan(z/2) + tan(z/2)tan(x/2) = 1 and just put in a b c in the equation in form of tan and got the answer.

[@reenabenpatel7916]

@@zeroplays9915 tum arjuna 1.0 se ho na?

[@ABHINAV_RAJPUT.07]

@@zeroplays9915 good approach brother

[@zeroplays9915]

@@reenabenpatel7916 no bro mai VMC ka hu

[@ashugarg3513]

I did it by using Am>= Hm inequality .. one step answer 😂

[@sonamsingh5762]

keep doing what you are doing...really best on you tube.. you literally teach straight from the heart...

[@Affiliatexraza]

Sir yeh question amu mai pochaa jata hai entrance test msi

[@Heymystif__]

It was an amazing question sir. Really it gives so much satisfaction when we get answer of these algebraic questions. Please keep uploading more of such videos😊

[@Baigan_ka_barta]

One of the most tricky question i've seen so far. Got it on the second try btw. We would love to see more questions like these. Love you sir❤❤❤

[@nandakumarcheiro]

Select the column matrics takin column matrics 1,2,-3 or 2,3 -5 al determinant becomes 9 as substitute and two multiples.

[@mishralal]

Let a= -1 , b= -2 , c=3 2 minutes method

[@saptakpaul8815]

I assumed a=1, b=2 and c=-3. The simplified the expression by putting their values and got 9. 😊😊

[@babitayadav4370]

That's pure algebra

[@a.kverma_6625]

That's the wrong way of doing it Try again bro

[@MSMINDIA100]

@@a.kverma_6625 Ya because this question was subjective so this method will be wrong..

[@khushpanara124]

This method can be used when it is objective, but in subjective this method will be invalid

[@ayonsingha6970]

The mighty assumtion method

[@Dharmarajan-ct5ld]

BEST example of essay writing..try to see substance of question..think first

[@IITJEE49]

Take values of a b and c as -1 -1 and 2

[@SumitSingh-wf9ih]

Nhi kar sakte bro

[@FineValkyrie]

U can't take as there is a-b in denominator so it will become something upon zero

[@parthsingh5875]

Sir honestly speaking I have attempted this question by 4 ways which I have in my mind but didnot get the answer they become very complex in the end .... But randomly I put 😂 a=3/4 b=-1/2 c=-1/4 And solve it within a second ❤❤❤❤❤❤❤❤🎉🎉🎉🎉🎉

[@parthsingh5875]

😂

[@Aryanshiva-he5ec]

SIR YOU ARE GENIUS OF MATHS

[@sirak_s_nt]

Ye question Allen ki Class 9 Advance Surds and Indices ke 2016 version me diya h.. Uske baad se toh hata diya..

[@HarshChauhanOfficial11]

Short trick (No. Of variable)^2 3^2 9

[@shakuntalasingh3178]

🙀

[@toxicgaming2020]

😂

[@VOM2230]

Legend of Mathematical world 🌍

[@akashsinghjadaun4776]

Simple sir 👍❤️😍

[@kj2.099]

Sir ur the best teacher of maths

[@RameshSharma-ps9pl]

Sir I have a doubt in a question please tell 🙏🙏🙏🙏 Please sir Question) prove that 1 - cos²A - cos²B - cos²C -2cosA.cosB.cosC = 4sin( A+B+C/2 ).sin (A+B-C/2).sin ( A-B+C/2).sin(C+B-A/2) Please tell sir

[@atharva5177]

What a beautiful question sir bring more such tough questions solutions

[@navodayanayush]

Hello sir Maine is question attempt diya khud se aur bahut hi aasani se ho gaya.. Isame a+b+c=0 hai to a+b=-c ho jayega. Aur is chiz pehale me c ke jagah par put Kar denge.. To sab kat ke -1 aa jayega aur usi Tarah se sab -1 aa jayega kul mila ke (-3)×(-3) =9

[@SAYED.ISLAM-7_86]

Sir I am very happy because I solve this by first attempt

[@fortune86]

Simply put -a-b in place of -c (from above equation), similarly do for -a and -b . We will get the answer in 2 steps

[@zeroplays9915]

i did it using trignometry, a=tan(x), b=tan(y), c=tan(z) and assuming x+y+z=180deg, so [tan(x)][tan(y)][tan(z)] = tan(x)tan(y)tan(z) and tan(x/2)tan(y/2) + tan(y/2)tan(z/2) + tan(z/2)tan(x/2) = 1 and just put in a b c in the equation in form of tan and got the answer.

[@anshandayan3972]

​@@zeroplays9915han bhai thik he samj Gaye 10 bar ek cheez ko sabke comment pe kyun likh rahe ho

[@speakingsarcasm9014]

Substitute a=3, b=-2, c=-1 or anything (not all zero) which makes a+b+c=0 such that no two of them are same.

[@Bloggers-ru2vp]

ssc?

[@gamingwithnoob69]

b-c/a=x c-a/b =y a-b/c=z Make this type of (x+y+z)1/x+1/y+1/z) eq 1 b-c=ax c-a=by a-b =zy add up all these then ax+by+cz=0 then ax +by +cy =a+b+c a(x-1)+b(y-1)+c(z-1)=0 Therefore x= y=z=1 Then put the value in eq 1 3*3=9 Is it right way to do it ?? If not please correct me

[@piyush3524]

How it became x=y=z= 1

[@subhadraprasad7676]

Hello sir,, kabhi NDA ke important questions par aesi video aane chahiye..

[@viwanjain7624]

There is another method.... kind of silly one but works!!.... Just put a=1 b=2 c=(-3).... Ans is 9.... I did it within a minute....😬😬

[@shawan7089]

Sir please teach for olympiads

[@debalinakoley-tf6ek]

Thanks a lot sir 🙏 ❤

[@pranaykandpal8464]

Sir plzzzz 11th ke sare chapters ke lecture dobara phir se naye Wale bana do plzzzzz sirrr... Agar chahiye to paid batch kar lijiye

[@SachinChaudhary-u3d]

Sir aap ka phone number kya he

[@Shubham_edits7890]

U can also put the value of b-c,c-a from the given equation a+b+c=0 from where by simplifying we get 9 answer

[@c.d7562]

Sir, If we take let, a=k b=2k c=-3k then , a+b+c=k+2k+(-3k) =0 Now,if we use these value In following question then we get ,9 ans My question is that This method may be consider as an another method, Please reply me if possible 🙏 This is subjective method or not

[@rupak07ambekar18]

The approach may give you the answer but imagine if the addition was in form of roots or complex numbers then assuming the variable K won't work, so if Mcq type comes you can apply your trick but in integer type you have to go with this method

[@kingkongffgamer2440]

You are the best maths teacher

[@prathnaiahsetty4601]

Question to bahut easy tha😂😂

[@sanyamagarwal6586]

2:36 khud ban gya maja bhi aagya Mera tarika alag tha par vo bhi sahi tha

[@Kpk476]

put a=1/3, b=2/3, c=-1

[@zeroplays9915]

i did it using trignometry, a=tan(x), b=tan(y), c=tan(z) and assuming x+y+z=180deg, so [tan(x)][tan(y)][tan(z)] = tan(x)tan(y)tan(z) and tan(x/2)tan(y/2) + tan(y/2)tan(z/2) + tan(z/2)tan(x/2) = 1 and just put in a b c in the equation in form of tan and got the answer.

[@marianne-wt8it]

Could you elaborate a bit

[@OmJain-wy6mh]

I am going in motion coaching i am in class 9th and this question is in our 2nd exericse

[@naveenkhare1979]

What a brilliant solutions of a typical expressions

[@serajmd3256]

Dear Sir mere pass two questions hai Pythagoras se related ap ke liye first ki world ka sabase chota area wala right triangle kon sa hai jiska area sabase Chhota ek natural number ho aur Pythagoras (a²+b²=c²) ko satisfy bhi kare note a,b,c irrational number na ho.for example 2²+1²=(√5)² yaha par to area 1 jo ki ek sabase chhota natural number toh hai lekin 'c' irrational number hai tino rational number yani tino p/q ke form me ham likh paye hona chahiye.second question 3²+4²=5² area 6 but see that( 7/10)²+(120/7)²=(1201/70)² isaka bhi area 6 hi hai kya ap ek aur(a,b,c) rational length bata sakate hai jiska area 6 hi ho aur a²+b²=c² ho jaha a,b,c, rational ho aur 1/2×ab=6 ho.

[@JEE-wt5od]

Maza aagya sir ❤❤ mujse solve hogya

[@jholibaba]

In each bracket we can operate with +3 and -3 we get -3 in both brackets which on multiplication get 9 💯

[@sheulydasgupta7131]

I also got the same.

[@himanshubaliyan5015]

kha se laate ho itna dimag kuch bhi karna nhi h isme toh. such a beautiful subject is maths you can make solution smaller to very longer as you want.

[@Manaschoudhary3636]

​@@himanshubaliyan5015Question is subjective

[@ABHINAV_RAJPUT.07]

Sir maja aa gya please aise questions aur layega 1st attempt me ho gya

[@anantupadhyay2832]

best way to solve this problem without putting the values was to multiply the terms simply and then add the terms with same denominator which could easily be solved by seeing the symmetry by this approach we can get rid of boring factorization

[@zeroplays9915]

i did it using trignometry, a=tan(x), b=tan(y), c=tan(z) and assuming x+y+z=180deg, so [tan(x)][tan(y)][tan(z)] = tan(x)tan(y)tan(z) and tan(x/2)tan(y/2) + tan(y/2)tan(z/2) + tan(z/2)tan(x/2) = 1 and just put in a b c in the equation in form of tan and got the answer.

[@ashugarg3513]

No best way is to use AM >= HM inequality

[@NisargShah-xb2zj]

​@@ashugarg3513coincidence. A+B+C = 0 means they are negative and positive. (As all 3 can't be 0) and AM GM HM is only applicable for positive integer I tried with that and yes u get the answer 9 (when equality holds) it only holds when b-c / a = c-a /b = a-b/c

[@ashugarg3513]

Sir simply AM>= HM kyu nahi laga sakte usse bhi answer 9 hi ara hai

[@Ipho2026]

Saare number positive hone chie jo yha nai h

[@RONI-vc4hm]

Question karka maza aa gaya sir..... 👍👍❤❤😇😇

[@minicube9537]

Sir,maja hi a gya........ Sir you are really greate😁😁😁😁🎉🎉🎉🎉🎉

[@RameshSharma-ps9pl]

Sir I have a doubt in a question please tell 🙏🙏🙏🙏 Please sir Question) prove that 1 - cos²A - cos²B - cos²C = 4sin( A+B+C/2 ).sin (A+B-C/2).sin ( A-B+C/2).sin(C+B-A/2) Please tell sir

[@ravisinha2165]

Olympiad batch start kro n sir❤ je

[@HARSHSHARMA-db9oh]

Kal mera chemistry ka test hai or ye maths ka addiction chuth hi nahi raha

[@amongus-xq8lu]

sir please do gaokao and integral bee series

[@rajeshpawar6271]

Feels happy in being in that 1% people

[@nilasutradhar7213]

Thank you sir very much

[@gauravaggarwal]

there are 2 brackets in first bracket, b=c then a=-2b=-2c putting these values first brackett becomes zero that means a=b,b=c,c=a are factors of first brackett and since its homogeneous fraction throughout so merely looking at it one can tell, that finally first brackett is of the form k (a-b)(b-c)(c-a)/abc now look at second brackett a=0 means b=-c which makes second brackett =0 hence second brackett which has all terms homogeneous will be m abc/(a-b)(b-c)(c-a) multiplying both brackets all the terms having a,b,c will cancel out. so till here merely looking at problem with logic you know it is constant. means invariant, now put a=2, b=1, c=-1 since we have already proved it is invariant or constant, which makes it 9 so you don’t need pen paper for this

[@gauravaggarwal]

homogeneity and cyclicity makes such problems very easy, as discussed in detailed solution I have written above. just use homogeneity cyclicity and invariance

[@genos1458]

You can't put a = 0 as it's not in the domain right ? In the first bracket a is in the denominator . Except for zero we can use any other value and your explanation is nice then .

[@gauravaggarwal]

@@genos1458 yes, my bad, put any number other than that, Thankyou

[@gauravaggarwal]

@@genos1458 edited

[@Bhawani143]

Yyeee.......I have solved this question and I feel very happy 😊🎉

[@ManishKumar-fy4dz]

Sir ek international Olympiad mai ek windmill wala ques krwa do apke style may maja aa jayega

[@PuduDevi]

Humare coaching ke teacher ne notes mein likhwaaya!! JEE!!

[@arunamanchikatla1716]

a=3,b=-2,c=-1 b-c not equal to c-a not equal to a-b not equal to 0 hence upon substitution we get 9

[@jeeadvanced4301]

Maine ye question 2 minute me bna liya 1 page only 😅😅😅 real

[@hemantbarde5367]

Sir kya ham iska answer random number likhke kar sakte hai kya exam me?

[@aditya_official647]

Yeh question to class 10 me tha hamara😂

[@bsbrawl1653]

sir maine first attempt mei 6 nikal diya with expanding and got 6 due to great mistake

[@ajityadav5300]

Many ways to solve this problem. This method is classic algebra love it..

[@a.kverma_6625]

SIR!!!! I solved this question in first attempt 😀😀🤯🤯 I just applied the general approach by taking LCM and so on and I unbelievable solved the question in 1st attempt. Sir you are the greatest mathematics teacher of all time And my inspiration is Ramanujan sir ❤❤ I am in class 10th Thank you sir

[@toxicgaming2020]

Juta kaha hai mera

[@a.kverma_6625]

​@@toxicgaming2020Apna pichwada check kar mil jayega. Aur agar barf wagera chahiye hoga to bol dena kyuki teri bahut jyada hi jal rahi hai

[@toxicgaming2020]

@@a.kverma_6625 oh my god bhai bura maan gya

[@a.kverma_6625]

@Manoj-sd3yi Thanks I appreciate it But you know I am not kind of intrested in Olympiad. I am interested in JEE ADVANCED and ngl I was able to solve some of JEE ADV. Trigonometry question (I am not lying) Also I usually don't see people like you who encourage the young bloods instead of making fun of them or becoming jealous of them. My best wishes to you sir have a great day Thanks

[@toxicgaming2020]

@@a.kverma_6625 u are really 10 class kid bro its sad that some people get to hear name of jee in class 12 and kids like u starts solving in class 10 😥😥

[@rdx_noob_786]

Sir kya hum ise a b aur c ki koi value rakh kar solve kar sakte

[@ankitavenue3590]

Russian physics and maths exams are on another level

[@shouryasrivastava4264]

Sir i have got the same answer by putting the values of a,b,c from given equation.....Than by simplifying each fraction by componendo and dividendo.....after that I have got a perfect square in the form -(c/b + a/c + b/a)^2 by taking lcm i have got a quadratic equation in the numerator....and if a+b+c =0 then there is a possibility that a=b=c then by putting these value in numerator.....i have got (a^3+b^3+c^3 /abc)^2 then i have got answer as 9 Jee 2025 aspirant ❤️

[@Rishabh-wc6fv]

It's wrong if a+b+c=0,then possibility can be a=b=c=0, not a=b=c

[@shouryasrivastava4264]

@@Rishabh-wc6fv both are the possibilities

[@shobhitkumar1108]

Sir i have an easy solution Since a+b+c=0 so b-c/a= b-c/-b-c=-(b+c/b+c)=-1 c-a/b=c-a/-c-a=-(c+b/c+b)=-1 a-b/c=a-b/-a-b=-(a+b/a+b)=-1 And a/b-c=-b-c/b-c=-(b+c/b+c)=-1 b/c-a=-c-a/c-a=-(c+a/c+a)=-1 c/a-b=-a-b/a-b=-(a+b/a+b)=-1 Now putting this value in equation [-1+(-1)+(-1)]×[-1+(-1)+(-1)] [-1-1-1]×[-1-1-1] [-3]×[-3]=9

[@diteshsingh9588]

What are you saying??? b-c/a = b-c/-b-c = -(b+c/b+c)??? Do check your dumb solution before posting it. Try multiplying (-1) to (b+c) it will result in -b-c not b-c.

[@shobhitkumar1108]

​@@diteshsingh9588 It's my fault I didn't check 😅

[@Jatinmishra829]

Sir aise question ke liye book kaha se le sar 😢😢

[@AlakMandal-di3ql]

Aman sir you are best

[@curioustechnique4600]

Bohot easy tha but maine thoda lengthy hogaya aur ans 9 aya but bohot hi maja ayaaaa sirji😻😻😻🎉🎊🙅

[@arunthegreat2009]

Sir can you tell the name of the book

[@santoshjaiswal179]

Love you sir ,love you math

[@debdasmukhopadhyay4692]

Fantastic.

[@funwithnandiniandrishi6095]

Easy question tha.... 9 hai answer ....btw thanks for boosting my confidence... simply brackets ko multiply bhi kar sakte hai

[@mahendrakumarpandey-mq7qb]

Sabhi me plus one karege aur plus 3 means minus bhi karege both equation and finally solve karege to numerator me a+b+c milega aur uski value zero hi finally minus 3 and minus 3 milega to plus 9 hoga

[@Aryanshiva-he5ec]

MY FAVROUTE MATHS SIR IS AMAN SIR

[@abhisag]

I solved it orally by inspection and answer is 9. Tell me if something is wrong with the reasoning. Given condition as well as expression are symmetric w.r.t a,b,c. So there is no reason that c-a/b could be different value than b-c/a etc. Hence, first factor in expression should be written as 3 x (b-c)/a. Similarly second becomes, 3 x a/(b-c). Product is 9.

[@rajendralekhwar4131]

Good one

[@sanjaykumar-ng6tv]

Amazing question

[@Arpanshukla12]

First sir love you bhannaat❤❤❤k

[@qualityyt]

Sir kya aap dpp har chapter ka provide kr sakte ho plz sir

[@softtechplus383]

Sir consider a+b+c=1+w+w^2=0 And put value in equation you will get 9 answer

[@shivanshushukla5284]

Let take , a=b-c ,b=c-a & c=a-b Then it satisfied a+b+c=0 Then put the value of only a , only b & only c the the fraction will cancel out and comes as 3*3 Which results 9

[@anilpratihast3242]

But, how you have taken a=b-c , b=c-a , c=a-b, Since, it is given that a+b+c=0, so, a = -b-c ; b= -c-a ; c = -a-b , so you cannot take the values as stated above. And if you say that after adding all the 3 equations, you are getting 0, then you should observe that *b-c+c-a+a-b=0* and not *a+b+c=0*, and you should observe that both of these are different equations. So, this can't be the observation for this question.

[@PhakerEdit]

Bro i got it in first attempt Class 9th

[@subratadebnath5436]

Nice problem 👌👌

[@anshgoyal3734]

We can just assume a=3, b=-2, c=-1 then solve it and easily it will solve

[@ΣΜΡΤΥ]

Want some unique jee related questions

[@allenite_585]

Me who is not able to solve simple algebraic questions and i solved this question in 5 mins. 😅

[@Mr_Cosmos_]

Did you solve this by yourself?

[@Manaschoudhary3636]

​@@Mr_Cosmos_ofcourse he is fakiing do you think he solved he said he dont able to solve simple and solving Olympiad?

[@Rising_night_676]

Sir maza to apko dekhe ke hi aa jata hai

[@alkgupta7015]

Just calculate the value for each using expression a+b+c = 0 a = -b -c b = -a -c c = -a -b Put this all values in given question and you'll get 9 The answer

[@spikee270]

A problem with many solutions

[@whites2]

I also used this

[@shiviitkgp]

Sir assumption method se bhi answer aa jayega

[@shivanshushukla5284]

Sir ek aur asan sa tarika h

[@dhruvbhalani5578]

Sir isme agar(a-b/c + b-c/a + c-a/b mein har ek mein +1 karde toh sirf do steps mein answer aa jayega

[@deeppatoliya4303]

Mahesh Kesvala aka Thugesh

[@abhinavrawat7999]

I am in class 9 and i solve this in my 2nd attempt love ur videos sir ❤️❤️

[@ravimohril7892]

Sir maja aa gaya factor karne ke baad halva ho gaya

[@ravimohril7892]

Sir maine bina open kiye cyclic se factor kiya