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-e6g4 ай бұрын
This is superb
@sampadsarkar27914 ай бұрын
It is very good and shortest,also easiest process .
@preciousmathematicsfun43314 ай бұрын
OMG, your method is very short
@Abby-hi4sf4 ай бұрын
@@preciousmathematicsfun4331 Thanks
@Abby-hi4sf4 ай бұрын
@@sampadsarkar2791 Thanks
@KojiLouis4 ай бұрын
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.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks but still same length trust me. It's not the shorter way
@Nithish00964 ай бұрын
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❤
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks so much for the contribution
@fabricejeanbayoro31784 ай бұрын
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
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks
@somaachakraborty20873 ай бұрын
(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
@deshbandhu774 ай бұрын
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.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks so much
@lusalalusala29662 ай бұрын
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.
@sundayalagbe91164 ай бұрын
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!
@JJONLINEMATHSCLASSchannel4 ай бұрын
Ok but I will advise you to Google it. You will see so many
@satyam-isical4 ай бұрын
Try an indian book "Pathfinder by V. Sheshan & Vikas Tiwari" It'll graze you upto international maths Olympiad level.
@jaykelkar71434 ай бұрын
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
@Zaidu9564 ай бұрын
I have a great trick to solve quickly! Just put a = 1, b = 2 and c = -3. This trick is applicable in most questions.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks
@anshumanpandey85474 ай бұрын
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.
@alfonsomzrt4 ай бұрын
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.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks for your contribution
@jensraab29024 ай бұрын
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. 🙂
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks so much . If you are my fan , you will notice that I break down my steps so that everyone will understand.
@jensraab29024 ай бұрын
@@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.
@ADN0Infinity4 ай бұрын
Owesome, keep it up❤️
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thank you, I will
@Xkwizit_P3 ай бұрын
Nice! Weldone
@JJONLINEMATHSCLASSchannel3 ай бұрын
Thank you! Cheers!
@YT90204 ай бұрын
There are two possible answers 2,-6
@JJONLINEMATHSCLASSchannel4 ай бұрын
Not really, watch and see
@gloriaorji3425 ай бұрын
Plz recommend a good maths textbook that will help someone pass o level mathematics.
@JJONLINEMATHSCLASSchannel5 ай бұрын
There are so many good maths text books. new general maths, New national maths, etc
@BN-hy1nd4 ай бұрын
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.🤩
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks for that!
@e-manny78194 ай бұрын
The first time I came across your channel. I like how you broke it down. Thank you for sharing your mathematical knowledge.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Glad it was helpful!
@Kay-ti7su4 ай бұрын
Can you solve more Olympiad
@JJONLINEMATHSCLASSchannel4 ай бұрын
Ok
@jajangsupajang54374 ай бұрын
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.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks for your observation. Only the solutions that are integers are required
@copter70134 ай бұрын
you only need 2 more if you want the exact values of a b and c
@saralgupta46784 ай бұрын
Just add and subtract 1 to the given expression
@vagabondtheinmate7094 ай бұрын
My sol B^2=a^2+c^2+2ac.. Sub dis in num and den , we get 2 as answer.
@dheypatel12644 ай бұрын
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
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks. But y the assumptions
@AbdoSabaique3 ай бұрын
Is b^2 - ac not zero?
@hazaaahmadhazaa27704 ай бұрын
Great work sister, from Tanzania
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thank you! 😃
@gloriaorji3425 ай бұрын
Plz are there topics one must read to pass o level mathematics. How can someone get NECO GCE scheme of work? Thanks.
@JJONLINEMATHSCLASSchannel5 ай бұрын
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)
@JJONLINEMATHSCLASSchannel5 ай бұрын
U can search online but am not sure of this
@tekestetesfazgi80784 ай бұрын
You are a good teacher with a nice handwriting
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thank you so much 😀
@mithilravirala40464 ай бұрын
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
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks so much for your contribution
@Crocodile9184 ай бұрын
Take a=1 b=1 and c=-2 we'll get answer
@sivaganesh24004 ай бұрын
Instead of these numbers u can use 1 ,-1,0...it can shorten ur method
@wizeman85324 ай бұрын
Nice question and good solution!❤
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thank you! 😃
@Combinedmathswithpraveen4 ай бұрын
This is nowhere near a math olympiad question
@oluwatosinakinpeloye51114 ай бұрын
Exactly
@nyonkavincenttafeli70024 ай бұрын
I agree with you
@eshuatbits4 ай бұрын
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
@oliviermouchart47514 ай бұрын
I agree too
@bruster81584 ай бұрын
agree with you
@saralgupta46784 ай бұрын
Just add and subtract 1 from the given expression
@JJONLINEMATHSCLASSchannel4 ай бұрын
Nice
@bravikumar89504 ай бұрын
Good explanation 👍👍👍
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks and welcome
@jamesluvisha54854 ай бұрын
I wish you were my mathematics teacher when I was in High school (Kenya)
@JJONLINEMATHSCLASSchannel4 ай бұрын
❤️❤️❤️
@OLALEKANADEBANJO-e6g4 ай бұрын
Putting into consideration the time given and ur solution,Time is gone already.
@JJONLINEMATHSCLASSchannel4 ай бұрын
🤣🤣🤣
@gbreel-11564 ай бұрын
Thank you very much my sister
@JJONLINEMATHSCLASSchannel4 ай бұрын
You are most welcome
@AbouTaim-Lille4 ай бұрын
The very most of the problems we encounter on KZbin are about calculous or Numbers theory,
@JJONLINEMATHSCLASSchannel4 ай бұрын
Noted
@mannatrana93614 ай бұрын
Let a= 1, b=2, c=-3 Ans 2 Done
@AmanSingh-xv1nx4 ай бұрын
I did it in my mind, this type of questions are very easy . I wonder if this is an actual Olympiad question.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks for your contribution
@shanukumar83814 ай бұрын
Put b=0 and a=1,c= -1 you will get answer easily
@oluwatosinakinpeloye51114 ай бұрын
And then again your explanation is true but kind of long and there are some steps that were not that necessary no offense
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks so much for your contribution
@bruster81584 ай бұрын
this is how to 6 line ques in 60 lines
@ainebyoonabright59734 ай бұрын
Well done ma❤
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks
@Onepiecetag4 ай бұрын
❤❤❤❤
@JJONLINEMATHSCLASSchannel4 ай бұрын
❤️❤️❤️
@ndivhuwomaseko62325 ай бұрын
Best mam ever...hw r you mam
@JJONLINEMATHSCLASSchannel5 ай бұрын
Am fine. Thank you
@Ahmed-kg2gf4 ай бұрын
The fact that u caan solve for b² in the equality u have then substitude it there and get the answer instantly
@satyam-isical4 ай бұрын
Head straight to the safe zone a=1,b=-1,c=0😂
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks
@avelandara38234 ай бұрын
b is the clue
@karonkanocharles80204 ай бұрын
NICE
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks
@themultiply66804 ай бұрын
In one minute 😂
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks
@LakshyaKapoorREALNOTREEL4 ай бұрын
I solved it mentally in under 50 seconds😂😂
@JJONLINEMATHSCLASSchannel4 ай бұрын
Wow
@EkomobongEtuk4 ай бұрын
Hmm nice
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks
@oluwatosinakinpeloye51114 ай бұрын
Yo which country are you from
@JJONLINEMATHSCLASSchannel4 ай бұрын
Nigeria
@padraiggluck29804 ай бұрын
So 3, -2, -1
@gloriaorji3425 ай бұрын
What is this maths Olympiad all about?
@JJONLINEMATHSCLASSchannel4 ай бұрын
Please Google it. You will get more information when you do that. Thanks for engaging
@chinchang51174 ай бұрын
Actually, for this kind of qn, there is a very simple trick. Let a = 2, let b = 3 and let c = -5.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks
@mulukentizazu-o1o2 ай бұрын
i love you❤
@amalbanerjee83172 ай бұрын
Answer will be 37.
@amalbanerjee83172 ай бұрын
Answer will be 2.
@Lost_in_nowhere4 ай бұрын
I did it in less than 30 sec😂😂🤣🤣
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks for your contribution
@khondwanibanda55374 ай бұрын
2 is the answer, now let me watch.
@JJONLINEMATHSCLASSchannel4 ай бұрын
But we are looking for 3 solutions. ❤️
@rozil27634 ай бұрын
Just take a=1,b=0,c=-1, fucking answer is their
@JJONLINEMATHSCLASSchannel4 ай бұрын
Please can you explain why we should assume or just assign those values and how
@jensraab29024 ай бұрын
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.
@rozil27634 ай бұрын
@@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
@technicaljav15264 ай бұрын
Substitute a=1 b=-1 c=0 tadaaa😂
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks but watch the video
@darkdoremon72974 ай бұрын
The fact that I am an Indian and solved it in 2 mins, is depressing, as I still can't crack JEE🤡
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks so much for your contribution
@sampadsarkar27914 ай бұрын
Long process.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks. Please drop your solution
@roohulbilal98474 ай бұрын
Taking too many steps.
@JJONLINEMATHSCLASSchannel4 ай бұрын
Thanks so much for your contribution. Please solve a shorter one for us. I would appreciate it. Thanks.