Solving an IMO Problem in 7 Minutes!! | International Mathematical Olympiad 2010 Problem 1

#IMO #FunctionalEquations #MathOlympiad

Here is the solution to IMO 2010 Problem 1!!

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I share Maths problems and Maths topics from well-known contests, exams and also from viewers around the world. Apart from sharing solutions to these problems, I also share my intuitions and first thoughts when I tried to solve these problems.

[ShefsofProblemSolving]

I also made a solution to this problem! Took me longer to solve the case f(0) = 0, my intuition usually doesn't like plugging in specific values into functions (x=y=1) unless I have nothing else to do. Now looking at your solution I can't believe I missed that (because getting f(1) = 0 solves the problem sub-case immediately)!

[shreyamjha]

Find all functions f such that f(x²)+f(x)*f(x+1)=0

Plz try and make a video for solution of this problem if you get time as I am stuck and if it's an easy one then reply with an hint .

[amartyabu]

#suggestion Hey! I like your channel and your quality of questions is great too. But, you need to work a bit on your explanation. Try to explain it in a simple way. Some parts you seem to miss on steps and it's hard to catch on. This is a genuine suggestion because i like your channel and i hope it grows. I hope you work on that

[dustinbachstein]

Nice solution, but I don't personally like this kind of exercises which look interesting and then only have trivial solutions...

[vijaybalajin]

Awesome
That too the selection of the questions

[krutarthshah]

I think the result is immediate by putting y=0
=> f(0) = f(x) [f(0)] for all x
=> f(x) = f(0)/[f(0)] or f(0) = 0
=> f(x) = [f(0)] + {f(0)} / [f(0)], {x} is the fractional part or f(0) = 0
=> f(x) = 1 + {f(0)}/[f(0)] or f(0) = 0
=> 1 <= f(x) < 2 or f(0) = 0
=> f(x) = 0 or k, where k belongs to [1, 2)
Did I miss something?
Great Video Nonetheless

[workstation]

f([[x]]×0)=f([x])×[f(0)]
or f([x]×1)=f(x)×f([1])
so
f(x)×f([1])=f(0)
thus f is constant if f(1) and f(0) are non zero

[NoxIITK]

I got f(x) = 0 and 1
Rest solution I missed😂

[jofx]

Seeing problem: confusion
Seeing answer:

[advaykumar]

Please solve this asap:f (x^2 +yf(x))=xf (x+y)

[iceblaze]

Please Anyone Can Help Me, Why We Have To Plug X = Y = 0 ?, How If X Doesn't Equal To Y ?

[euler]

Thinking critically, you're not *really* solving it in 7 minutes are you? Being able to solve it on paper in 7 minutes, 11 years after the question has been published and with all that time to ruminate over the result - and being able to solve the problem in 7 minutes totally unseen in the pressure of an exam setting are two completely different things.

It's a nice solution, yes - and yes, it is presented in 7 minutes - but titles of this sort of are little disingenuous and annoying.

[mittaldalal]

Presentation is not very clear. Not impressed.