Students In China Had To Solve This Before International Olympiad
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- เผยแพร่เมื่อ 15 ก.ค. 2023
- Solve This Before International Olympiad
Today we will be solving an interesting Algebra Problem
This question looks easy at the first glance, but gets interesting once you start to solve it.
Observation and calculation speed are very important when solving algebra related questions.
Now think where exactly do we need to find the answer to this interesting algebra problem
Please attempt this question at least once before watching this video.
Let's see how Aman sir attempts this question and gets the correct answer.
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#BhannatMaths #AmanSirMaths #algebra #olympiadmath - บันเทิง
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
nice one bro
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.
@@kindafool4083yeah but u can do 3x*3/x=9 n the method works
@@Therapoetic right, yeah
Wrong imagine if x was 1 it means b-a=c
Ek Arsa beet Gaya lekin Aman sir Aaj bhi best hi hai❤❤❤😊😊😊😊😊😊
My most favourite maths teacher on TH-cam. Lots and lots of thanks sir ❤❤😊
The satisfaction you well when you solve the question in your first try.. Is unmatchable❤.. 🙃
sir i solved it in first attempt
and it was a nice experience
keep bringing such question
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.
@@zeroplays9915it is mentioned in Sl loney
I assumed a=1, b=2 and c=-3. The simplified the expression by putting their values and got 9. 😊😊
That's pure algebra
That's the wrong way of doing it
Try again bro
@@a.kverma_6625 Ya because this question was subjective so this method will be wrong..
This method can be used when it is objective, but in subjective this method will be invalid
The mighty assumtion method
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😊
keep doing what you are doing...really best on you tube.. you literally teach straight from the heart...
Sir yeh question amu mai pochaa jata hai entrance test msi
What a beautiful question sir bring more such tough questions solutions
Select the column matrics takin column matrics 1,2,-3 or 2,3 -5 al determinant becomes 9 as substitute and two multiples.
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... 😀
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.
@@zeroplays9915 tum arjuna 1.0 se ho na?
@@zeroplays9915 good approach brother
@@reenabenpatel7916 no bro mai VMC ka hu
I did it by using Am>= Hm inequality .. one step answer 😂
SIR YOU ARE GENIUS OF MATHS
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
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❤❤❤
Sir ur the best teacher of maths
Ye question Allen ki Class 9 Advance Surds and Indices ke 2016 version me diya h.. Uske baad se toh hata diya..
BEST example of essay writing..try to see substance of question..think first
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.
Thanks a lot sir 🙏 ❤
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
Legend of Mathematical world 🌍
What a brilliant solutions of a typical expressions
Short trick
(No. Of variable)^2
3^2
9
🙀
😂
You are the best maths teacher
Let
a= -1 , b= -2 , c=3
2 minutes method
Take values of a b and c as -1 -1 and 2
Nhi kar sakte bro
U can't take as there is a-b in denominator so it will become something upon zero
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
Sir please teach for olympiads
Many ways to solve this problem. This method is classic algebra love it..
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.
ssc?
Sir plzzzz 11th ke sare chapters ke lecture dobara phir se naye Wale bana do plzzzzz sirrr...
Agar chahiye to paid batch kar lijiye
Sir aap ka phone number kya he
Sir maja aa gya please aise questions aur layega
1st attempt me ho gya
sir please do gaokao and integral bee series
Aman sir you are best
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
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.
@@zeroplays9915han bhai thik he samj Gaye 10 bar ek cheez ko sabke comment pe kyun likh rahe ho
Sir I am very happy because I solve this by first attempt
Thank you sir very much
Sir consider a+b+c=1+w+w^2=0
And put value in equation you will get 9 answer
put a=1/3, b=2/3, c=-1
Hello sir,, kabhi NDA ke important questions par aesi video aane chahiye..
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
homogeneity and cyclicity makes such problems very easy, as discussed in detailed solution I have written above.
just use homogeneity cyclicity and invariance
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 .
@@genos1458 yes, my bad, put any number other than that, Thankyou
@@genos1458 edited
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....😬😬
Question karka maza aa gaya sir..... 👍👍❤❤😇😇
Amazing question
Fantastic.
Sir kya aap dpp har chapter ka provide kr sakte ho plz sir
Question to bahut easy tha😂😂
Good one
Nice problem 👌👌
Sir ek international Olympiad mai ek windmill wala ques krwa do apke style may maja aa jayega
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.
Could you elaborate a bit
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
Yyeee.......I have solved this question and I feel very happy 😊🎉
Olympiad batch start kro n sir❤ je
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
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
How it became x=y=z= 1
Maza aagya sir ❤❤ mujse solve hogya
Sir maza to apko dekhe ke hi aa jata hai
Love you sir ,love you math
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
Juta kaha hai mera
@@toxicgaming2020Apna pichwada check kar mil jayega.
Aur agar barf wagera chahiye hoga to bol dena kyuki teri bahut jyada hi jal rahi hai
@@a.kverma_6625 oh my god bhai bura maan gya
@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
@@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 😥😥
In each bracket we can operate with +3 and -3 we get -3 in both brackets which on multiplication get 9 💯
I also got the same.
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.
@@himanshubaliyan5015Question is subjective
Simply put 1 2 and -3
Sir kya hum ise a b aur c ki koi value rakh kar solve kar sakte
Sir ek aur asan sa tarika h
Sir simply AM>= HM kyu nahi laga sakte usse bhi answer 9 hi ara hai
Saare number positive hone chie jo yha nai h
Sir,maja hi a gya........
Sir you are really greate😁😁😁😁🎉🎉🎉🎉🎉
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
Maza aagaya.... Got the answer!
I have seen this type question in 2019 RMO paper. Not same but similar pattern.
Sir can you tell the name of the book
Kal mera chemistry ka test hai or ye maths ka addiction chuth hi nahi raha
2:36 khud ban gya maja bhi aagya
Mera tarika alag tha par vo bhi sahi tha
Yea i also got 9, the proble was easier than expected, For that second part i didnt use the way that sir used , i just facotirzed and used a63+b63+c^3=3abc and in 6 steps i got 9abc/(a-b)(c-a)(b-c) and these all got cancelled with the 1st part and hence got 9
Brilliant
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
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
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
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.
No best way is to use AM >= HM inequality
@@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
Sir assumption method se bhi answer aa jayega
Easy question tha.... 9 hai answer ....btw thanks for boosting my confidence... simply brackets ko multiply bhi kar sakte hai
Sir aise question ke liye book kaha se le sar 😢😢
First I take the values of a,b,c from equation ( a+b+c=0),and then putting into the ques,then I got answer 9 easily in first attempt in the begining of the video
Sir it can be done very easily by a3+b3+c3 = 3abc identity, because a+b+c = 0
So according to you a+b=O And and Accordingly to you A^2+b^2=O ?
@@user-yi5cc9wn5c nahh, it is an identity I'm not saying a+b = 0 ,it is given in the question that a+b+c=0 so we can use the identity I mentioned
Want some unique jee related questions
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 ❤️
It's wrong if a+b+c=0,then possibility can be a=b=c=0, not a=b=c
@@Rishabh-wc6fv both are the possibilities
Sir please launch a proper batch for olympiad
MY FAVROUTE MATHS SIR IS AMAN SIR
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
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.
Maja aa gaya sir ji
put a=3,b=-2 and c=-1 and find value
sir maza aa gaya maine aaj meri 3rd tst ki problem ki.
5 min me ho gaya
Sir, I have solved this without seeing the solution but I have got 6-(-3) at last
Sir pls make a solution video on this question ie. x tends to 0 ((e^x+e^-x-2)/x^2)^(1/x^2) pls sir solve this it's my birthday gift from you ❤
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
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.
@@diteshsingh9588 It's my fault I didn't check 😅
put w and w^2 and 1 you will get the answer
Just put 3 , -2,-1
And calculate answer
Maza aagaya dil mage more
Idhar AM GM se bhi to KAAM hojayega na? the expression is like (x+y+z)(1/x+1/y+1/z) which is >= 9.... So its minimum value will be 9.. And will be true when x = y = z....
Very good approach bhai but how you minimum is ans 😅 and also how u know that every term is positive
Every term can never be positive as their sum is 0, atleast one no. Has to be -ve
=> AM, GM is wrong approach
Feels happy in being in that 1% people
There is no need to do all this rut.Simply choose a=1,b=2 and c=-3 and find the value of the expression to be 9.
Sabse aasan a=3 b=-2 c = -1 put karo ans aa jayega
Kudse ho geya sir .bohot Maja aya