A Nice Olympiad Cubic Problem | MATHEMAGIC

You're presented with a CUBIC equation with
x^3 - x^2 = 100
It's kind of tricky because we have a general formula for quadratics but not for cubics, so how do we get around that in Mathematics? 🙄
🟢 You could use a graphic solution with your GDC or DESMOS
🔵 You can use Synthetic Division to turn it into a Quadratic
In this video we show you how this all works out
Please like, share and subcribe to support the Channel!
#exponents #logarithm #solve
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[@thiagocoelho5824]

An interesting way to find that 5 is a solution would be rewriting the equation as x^2(x-1) = 100 and looking for the divisors of 100. We have that 100 = 50x2 (nothing like x^2(x-1)), but 100 = 25x4 gives us 5^2(5-1), hence 5 is a solution.
Nice problem and video, by the way!

[@themathemagicchannel]

Absolutely, so many ways to get there and your way is elegant and sound, thank you for sharing

[@IainDavies-z2l]

But can you solve 1/76 scale weight of 126t?

[@themathemagicchannel]

😅

[@osiraben179]

Is that a joke? Could you please explain it me. I learn English, don't understand well.

[@IainDavies-z2l]

No not a joke, I have a model railway and want to know what the scale weight of model trains should be but nobody can answer the question. I know the answer but want to see if anyone else can.

[@themathemagicchannel]

126/76? Approx 1.66t?

[@IainDavies-z2l]

For the scale weight in 1/76 you multiply the prototype weight by 2.49, so if a class 66 weight is 126t the scale weight is 312g. So for each ton you multiply by 2.49 and that gives you the scale weight in grams.