A trending math OLYMPIAD question.

A maths OLYMPIAD question. No calculator is allowed.

[Abby-hisf]

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

[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.

[sundayalagbe]

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!

[somaachakraborty]

(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

[fabricejeanbayoro]

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

[Nithish]

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❤

[lusalalusala]

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.

[Outfotech]

I enjoy most of your videos, I haven't seen stuff on calculus and matrices are you doing them as well?

[jensraab]

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. 🙂

[e-manny]

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

[deshbandhu]

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.

[BN-hynd]

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.🤩

[tekestetesfazgi]

You are a good teacher with a nice handwriting

[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.

[Zaidu]

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

[jajangsupajang]

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.

[gloriaorji]

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

[Combinedmathswithpraveen]

This is nowhere near a math olympiad question

[gloriaorji]

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

[AbouTaim-Lille]

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