Germany Math Olympiad, a system of cubic equations

This question is question 1 from the 2015 Germany math olympiad contest. I love the fun and creative system of equations!


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[jonathangrey]

“Let me put y blue.”

“No why would I do that, I’m blackpenredpen.”

[YoshBruh]

"You guys should try and solve first"


Me at 3 am: No, no I dont think I will

[myrus]

6:30 instead of doing polynomial division, if you add y - y and split the -2y^2 into -y^2 and -y^2 you get (y^3 - y^2) - (y^2 - y) - (y + 1). You can now see that you can take out a (y-1) from each of those.


I got this, but admittedly I did do the polynomial division first then looked for a prettier solution once I knew the end result, but it’s still cool imo: A reminder that factoring non-obvious polynomials like this is in some ways about “creating or finding the symmetry” which I think is a helpful way to look at it for other factoring problems too.

[shahbazsheikh]

The seamless switching of the pens was just as impressive as the math.

[julianmejiac]

6:32, I called this "Ruffini's rule", a particular version of "Horner's method" ( usually called synthetic division). I remembered I learned this in highschool, and I used to do it without thinking. Then I understood, how division of polynomials work, and never used it again until the point I completely forgot about the algorithm.

[friendtilldawn]

just like almost every single math problem u start losing urself throughout the process and question if 1 + (-1) is 0 :))

[pkmath]

Shout out! "DO NOT Automatically substitute!" Haha especially differential equation. I like your pi. Would like to buy that one

[thesixteenthstudent]

imagine you saw 9 as "a" and tried to solve problem like 1 hours ...

[henrique]

Man I love the solutions you bring, they are always so fun to see!

[osmeridium]

This video is very mathematically satisfying

[przemezio]

First try: check if x=1, y=1
Result: it works 😳
Conclusion: I am a god.

Greetings from Poland 🇵🇱 (now, it's 3.57 AM here, so I should go sleep 😴).

[linguinelabs]

This is my favourite content. These videos are keeping my math fresh while in quarantine. Thank you for making these!

[vari]

Glad to see 3b1b spreading around just as well as *the thing*

[eleazaralmazan]

Nice! The solution presented in this video is super elegant!

[idrisShiningTimes]

Great video. My expansions concept got cleared! Thanks!

[rohitjacob]

What I did is that I first took x^3 common from the first equation and y^3 from the 2nd.Now I took (y/x) as some value 'a' and divided the two equations.When we simplify this we get a cubic equation having only the value 'a'. If u solve that equation, we get many more terms like the solutions of x^3 = 1 and y^3 = 1 and some more, which also includes the answers u found.But yours was an elegant method and much more easier. Great videos btw

[dmitryweinstein]

Man, you use colours so well! A very efficient lecturer, too...

[younesabid]

Grant would be proud of your new microphone :)

[jkstudyroom]

Nicely done sir! Really like your videos!!!

[chillfrost]

about the division made in 8:00, I can affirm that in Portugal, my country, we learn it in high school (10th grade), but it is called as Ruffini's Rule