A trending math OLYMPIAD question.

[@Abby-hi4sf]

a + b + c = 0 a + c = -b ( squre both side) (a + c)^2 = (-b)^2 a^2 + c^2 + 2ac = b^2 shift 2ac and add b^2 on both side a^2 + b^2 + c^2 = 2b^2 - 2ac take common fator 2 on the right side a^2 + b^2 + c^2 = 2(b^2 - ac) divide both side by (b^2 - ac), the answer is 2

[@OLALEKANADEBANJO-e6g]

This is superb

[@sampadsarkar2791]

It is very good and shortest,also easiest process .

[@preciousmathematicsfun4331]

OMG, your method is very short

[@Abby-hi4sf]

@@preciousmathematicsfun4331 Thanks

[@Abby-hi4sf]

@@sampadsarkar2791 Thanks

[@KojiLouis]

Very good solution. In this type of problem I recommend solving for one of the variables and then substituting back into the fraction to eliminate one of the variables. Solving for c gives c= -a - b. Substitute for c into the fraction. Then you will get a fraction with only two variables of a and b. Expand and simplify the numerator and denominator and you will find your answer of 2 rather quickly.

[@JJONLINEMATHSCLASSchannel]

Thanks but still same length trust me. It's not the shorter way

[@Nithish0096]

a+ b+ c=0 a+c=-b Then from a'2 + c'2 +b'2 ÷ b'2 -ac Use this formula a'2+ c'2=(a+c)'2 - 2ac in above fraction. (a+c)'2 - 2ac + b'2 ÷ b'2 -2ac ( -b)'2 + b'2 -2ac ÷ b'2 -2ac b'2 + b'2 - 2ac ÷b'2 - 2ac 2b'2 - 2ac/b'2- 2ac Then take out the common factor 2 and strick out the variables Hence the answer is 2 in❤

[@JJONLINEMATHSCLASSchannel]

Thanks so much for the contribution

[@fabricejeanbayoro3178]

Very good explanation as you go through the solution, that's a trait of a great teacher. 8:03 Just factorise -1 from the two terms in the brackets in the RHS. A faster solution would have been to make a + c the subject, squaring both sides and proceed from there. (a + c)^2 = (-b)^2

[@JJONLINEMATHSCLASSchannel]

Thanks

[@somaachakraborty2087]

(a+c)²=b² a²+b²+c²-2ac+2ac (a+c)²-2ac+b² b²+b²-2ac 2(b²-ac) a²+b²+c²/(b²-ac) =2 As simple as that

[@deshbandhu77]

Another way to quickly solve the problem is a=-1 , b=-1 , c=2 . Ofcourse the assumption here is the result is independent of a,b,c . hence any combination which satisfies a+b+c=0 shall give you the same value.

[@JJONLINEMATHSCLASSchannel]

Thanks so much

[@lusalalusala2966]

Before solving this problem, one has to assume that the case a=b=c=0 is excluded. When this case is excluded, b^2 will never be equal to ac. Therefore, the ratio will be 2 as presented or as @Abby-hi4sf did it the simple way.

[@sundayalagbe9116]

Nice Work! A down to earth approach! Please help recommend resource materials and/or links for Olympiad/Gifted Mathematics Exams. Both Prep Materials and Past Questions. Thanks!

[@JJONLINEMATHSCLASSchannel]

Ok but I will advise you to Google it. You will see so many

[@satyam-isical]

Try an indian book "Pathfinder by V. Sheshan & Vikas Tiwari" It'll graze you upto international maths Olympiad level.

[@jaykelkar7143]

If this is an identity...it works for ALL values of a b c ....so you can put a = 2 b,c = -1 to solvee... correct me if im wrong guys

[@Zaidu956]

I have a great trick to solve quickly! Just put a = 1, b = 2 and c = -3. This trick is applicable in most questions.

[@JJONLINEMATHSCLASSchannel]

Thanks

[@anshumanpandey8547]

This is not a trick but a very logical approach. We have only one constraint on the values of a,b & c which is a+b+c=0. So all the values which satisfy the given constraint are valid and the seemingly complex expression can be evaluated using them. If there were more constraints on a,b&c ,you would just use values that satisfy all given constraints. There is mostly never a need of fancy formulas to find the value of a given expression in such cases.

[@alfonsomzrt]

im just going to go with a = -(b+c) and you can substitute it within the problem, you got it 2, using some manipulations and algebraic identities.

[@JJONLINEMATHSCLASSchannel]

Thanks for your contribution

[@jensraab2902]

That's a really nice problem! It's kind of simple once you know how to do it but that's always the case with this kind of problems, isn't it? 😅 I guess some students will know that (a+b+c)² expands to a²+b²+c²+2(ab+ac+bc) so this would save various steps; also I think the kind of student to tackle this problem should know that at 8:13 you can get b²-ac by extracting -1 from -b²+ac, no need to expand, IMHO. But that's nitpicking and maybe those who learn math will profit from the more explicit steps. Personally, I didn't see that factorizing the ab+ac+bc part would be beneficial because I didn't think of using a+b+c=0 to do the a+c=-b substitution! I felt a little stupid when I saw what you did. Again, nice problem. 🙂

[@JJONLINEMATHSCLASSchannel]

Thanks so much . If you are my fan , you will notice that I break down my steps so that everyone will understand.

[@jensraab2902]

@@JJONLINEMATHSCLASSchannel I've stumbled across your videos only recently. If you want to make the steps clear for everybody, I think you're doing a great job! I didn't mean to criticize you; you know your audience better than I do! 😀 Hope your audience keeps getting bigger.

[@ADN0Infinity]

Owesome, keep it up❤️

[@JJONLINEMATHSCLASSchannel]

Thank you, I will

[@Xkwizit_P]

Nice! Weldone

[@JJONLINEMATHSCLASSchannel]

Thank you! Cheers!

[@YT9020]

There are two possible answers 2,-6

[@JJONLINEMATHSCLASSchannel]

Not really, watch and see

[@gloriaorji342]

Plz recommend a good maths textbook that will help someone pass o level mathematics.

[@JJONLINEMATHSCLASSchannel]

There are so many good maths text books. new general maths, New national maths, etc

[@BN-hy1nd]

Wow, it looks simple after it as been done. The challenge is being able to think ahead before it is done. So, ignore the criticisms. Well done.🤩

[@JJONLINEMATHSCLASSchannel]

Thanks for that!

[@e-manny7819]

The first time I came across your channel. I like how you broke it down. Thank you for sharing your mathematical knowledge.

[@JJONLINEMATHSCLASSchannel]

Glad it was helpful!

[@Kay-ti7su]

Can you solve more Olympiad

[@JJONLINEMATHSCLASSchannel]

Ok

[@jajangsupajang5437]

I'm curious. How can 1 equation with 3 unknown variables can be solved. The result will be many combinations. Need 2 more equations to be exact. CMIIW.

[@JJONLINEMATHSCLASSchannel]

Thanks for your observation. Only the solutions that are integers are required

[@copter7013]

you only need 2 more if you want the exact values of a b and c

[@saralgupta4678]

Just add and subtract 1 to the given expression

[@vagabondtheinmate709]

My sol B^2=a^2+c^2+2ac.. Sub dis in num and den , we get 2 as answer.

[@dheypatel1264]

a+b+c=0 a=-1 b=2 c=-1 a square + b square + c square equals to 6 and b square minus ac gives 3 which further gives 2 easy man

[@JJONLINEMATHSCLASSchannel]

Thanks. But y the assumptions

[@AbdoSabaique]

Is b^2 - ac not zero?

[@hazaaahmadhazaa2770]

Great work sister, from Tanzania

[@JJONLINEMATHSCLASSchannel]

Thank you! 😃

[@gloriaorji342]

Plz are there topics one must read to pass o level mathematics. How can someone get NECO GCE scheme of work? Thanks.

[@JJONLINEMATHSCLASSchannel]

To pass u need to get the curriculum for Waec, neco, gce etc and that can be gotten from a principal of any secondary school. But I will advice you study well from ss1 to ss3 curriculum and then solve past questions as well (very important)

[@JJONLINEMATHSCLASSchannel]

U can search online but am not sure of this

[@tekestetesfazgi8078]

You are a good teacher with a nice handwriting

[@JJONLINEMATHSCLASSchannel]

Thank you so much 😀

[@mithilravirala4046]

Lot of people are saying she is taking a lot of time it is because she is explaining to us there is no way a olympiad level teacher would take so long to evaluate (a+b+c) ^2. PS :- for me it looks like 6th class olympiad question

[@JJONLINEMATHSCLASSchannel]

Thanks so much for your contribution

[@Crocodile918]

Take a=1 b=1 and c=-2 we'll get answer

[@sivaganesh2400]

Instead of these numbers u can use 1 ,-1,0...it can shorten ur method

[@wizeman8532]

Nice question and good solution!❤

[@JJONLINEMATHSCLASSchannel]

Thank you! 😃

[@Combinedmathswithpraveen]

This is nowhere near a math olympiad question

[@oluwatosinakinpeloye5111]

Exactly

[@nyonkavincenttafeli7002]

I agree with you

[@eshuatbits]

This can be changed to a nice question by taking 2+2+2 in rhs and 3 symmetric in lhs Also divide everything by a2+b2+c2

[@oliviermouchart4751]

I agree too

[@bruster8158]

agree with you

[@saralgupta4678]

Just add and subtract 1 from the given expression

[@JJONLINEMATHSCLASSchannel]

Nice

[@bravikumar8950]

Good explanation 👍👍👍

[@JJONLINEMATHSCLASSchannel]

Thanks and welcome

[@jamesluvisha5485]

I wish you were my mathematics teacher when I was in High school (Kenya)

[@JJONLINEMATHSCLASSchannel]

❤️❤️❤️

[@OLALEKANADEBANJO-e6g]

Putting into consideration the time given and ur solution,Time is gone already.

[@JJONLINEMATHSCLASSchannel]

🤣🤣🤣

[@gbreel-1156]

Thank you very much my sister

[@JJONLINEMATHSCLASSchannel]

You are most welcome

[@AbouTaim-Lille]

The very most of the problems we encounter on KZbin are about calculous or Numbers theory,

[@JJONLINEMATHSCLASSchannel]

Noted

[@mannatrana9361]

Let a= 1, b=2, c=-3 Ans 2 Done

[@AmanSingh-xv1nx]

I did it in my mind, this type of questions are very easy . I wonder if this is an actual Olympiad question.

[@JJONLINEMATHSCLASSchannel]

Thanks for your contribution

[@shanukumar8381]

Put b=0 and a=1,c= -1 you will get answer easily

[@oluwatosinakinpeloye5111]

And then again your explanation is true but kind of long and there are some steps that were not that necessary no offense

[@JJONLINEMATHSCLASSchannel]

Thanks so much for your contribution

[@bruster8158]

this is how to 6 line ques in 60 lines

[@ainebyoonabright5973]

Well done ma❤

[@JJONLINEMATHSCLASSchannel]

Thanks

[@Onepiecetag]

❤❤❤❤

[@JJONLINEMATHSCLASSchannel]

❤️❤️❤️

[@ndivhuwomaseko6232]

Best mam ever...hw r you mam

[@JJONLINEMATHSCLASSchannel]

Am fine. Thank you

[@Ahmed-kg2gf]

The fact that u caan solve for b² in the equality u have then substitude it there and get the answer instantly

[@satyam-isical]

Head straight to the safe zone a=1,b=-1,c=0😂

[@JJONLINEMATHSCLASSchannel]

Thanks

[@avelandara3823]

b is the clue

[@karonkanocharles8020]

NICE

[@JJONLINEMATHSCLASSchannel]

Thanks

[@themultiply6680]

In one minute 😂

[@JJONLINEMATHSCLASSchannel]

Thanks

[@LakshyaKapoorREALNOTREEL]

I solved it mentally in under 50 seconds😂😂

[@JJONLINEMATHSCLASSchannel]

Wow

[@EkomobongEtuk]

Hmm nice

[@JJONLINEMATHSCLASSchannel]

Thanks

[@oluwatosinakinpeloye5111]

Yo which country are you from

[@JJONLINEMATHSCLASSchannel]

Nigeria

[@padraiggluck2980]

So 3, -2, -1

[@gloriaorji342]

What is this maths Olympiad all about?

[@JJONLINEMATHSCLASSchannel]

Please Google it. You will get more information when you do that. Thanks for engaging

[@chinchang5117]

Actually, for this kind of qn, there is a very simple trick. Let a = 2, let b = 3 and let c = -5.

[@JJONLINEMATHSCLASSchannel]

Thanks

[@mulukentizazu-o1o]

i love you❤

[@amalbanerjee8317]

Answer will be 37.

[@amalbanerjee8317]

Answer will be 2.

[@Lost_in_nowhere]

I did it in less than 30 sec😂😂🤣🤣

[@JJONLINEMATHSCLASSchannel]

Thanks for your contribution

[@khondwanibanda5537]

2 is the answer, now let me watch.

[@JJONLINEMATHSCLASSchannel]

But we are looking for 3 solutions. ❤️

[@rozil2763]

Just take a=1,b=0,c=-1, fucking answer is their

[@JJONLINEMATHSCLASSchannel]

Please can you explain why we should assume or just assign those values and how

[@jensraab2902]

You are right that plugging in three arbitrary values will always give the right answer (as long as b²-ac≠0) because the result is independent from a, b, and c. The problem, though, is that you haven't proven that it is always the case. Yet, in math you'll need to show why it is you'll always be 2 as result. And obviously this method only works because the result is indeed independent of the variables. Imagine the result would be (a+b)/c or something like that, then you'd have to take a good number of combinations and try to figure out a pattern - and you still wouldn't have proofed the result.

[@rozil2763]

@@JJONLINEMATHSCLASSchannel because given questions have only one condition,and any number which satisfy give you answer , imagine if their are two given condition then you needed take numbers which satisfy both conditions

[@technicaljav1526]

Substitute a=1 b=-1 c=0 tadaaa😂

[@JJONLINEMATHSCLASSchannel]

Thanks but watch the video

[@darkdoremon7297]

The fact that I am an Indian and solved it in 2 mins, is depressing, as I still can't crack JEE🤡

[@JJONLINEMATHSCLASSchannel]

Thanks so much for your contribution

[@sampadsarkar2791]

Long process.

[@JJONLINEMATHSCLASSchannel]

Thanks. Please drop your solution

[@roohulbilal9847]

Taking too many steps.

[@JJONLINEMATHSCLASSchannel]

Thanks so much for your contribution. Please solve a shorter one for us. I would appreciate it. Thanks.