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Can You Solve This One?

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In this video, you will learn how to solve an awesome equation that was given at a German Math Olympiad.
Don’t forget to like the video and subscribe to @Aleksmatics so you never miss an update. Thank you!
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Опубликовано:

6 сен 2024

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Комментарии : 24

@HienNguyenHMN Месяц назад

Brute force?! I thought there would be a trick!

@Aleksmatics Месяц назад

@HienNguyenHMN so did I when I first saw it, but then I noticed that using brute force is not that hard.

@bucsredsoxredwings Месяц назад

In over 25 years of Math Olympiad, also international, I never encountered imaginary solutions. From which year and stage is it?

@Aleksmatics Месяц назад

I don't know. I was only told that this problem was given at an Olympiad in Germany.

@bucsredsoxredwings Месяц назад

@@Aleksmatics OK. Yeah I doubt it´s from Germany since we do not have the imaginary numbers in school throughout Germany. And the German committee also loves to only have integers as answers, not even real numbers to often.

@renesperb 2 месяца назад

The only real solution which needs no calculation because it is obvious : x = 0 .There are also two imaginary solutions which need some work.

@Aleksmatics 2 месяца назад

Correct.

@Ligatmarping 2 месяца назад

Anyway it needs some calculation to verify that there's no other real answer. One can by eye know that you get a cubic with 0 as a root so there will be a quadratic left.

@Aleksmatics 2 месяца назад

@@Ligatmarping true. Do you like such problems?

@Ligatmarping Месяц назад

@@Aleksmatics oh yes, Im a math teacher in an Argentinian university and as a kid I've been to lots of math olympiads. I always tend to try any kind of problem I see in youtube or other social sites haha.

@wobaguk Месяц назад

Im not actually sure it counts as 'solving it', but you can trivially observe just looking at the quotient, that if x is 0, you have the same product in the numerator and denominator as 4 negatives in product give a positive. I wonder if that would have counted in an olympiad or if its 'show your workings' kind of deal.

@Aleksmatics Месяц назад

X=0 is indeed an obvious solution, but it's not the only solution. Nevertheless, my guess is that you would get a point for it at an olympiad.

@mikeburns6603 2 месяца назад

Zero, inf and -inf also work.

@Aleksmatics 2 месяца назад

Inf and -inf don't work.

@mikeburns6603 2 месяца назад

@@Aleksmatics LIm x->inf gives 1. Try it.

@Aleksmatics Месяц назад

@mikeburns6603 infinities are tricky. If x=inf (or -inf), we'll end up with inf/inf, which is ill defined, not 1.

@kostasch5686 Месяц назад

lim x-> inf will give 1, x=inf will not give 1 because inf is not a number, its a limit and It cannot be the solution to an equation unless you re seeking solutions that contain inf to its set, which is pretty wonky and pretty much not applicable.

@mikeburns6603 Месяц назад

@@kostasch5686 The problem statement did not say reals only. Therefore the lim x->inf is a perfectly good solution.