A Very Nice Math Olympiad Question | How to solve x^2-x^3=12 | Algebra

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See the way I breakdown the solution of this question. There is a lot you can learn from this video.
How to solve x^2-x^3=12. ENJOY
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1 окт 2024

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Комментарии : 38

@cyruschang1904 5 месяцев назад

x^2 - x^3 = 12 x^3 - x^2 + 12 = 0 (x + 2)(x^2 - 3x + 6) = 0 x = -2, (3 +/- i✓15)/2

@GoatedGamer-v7n 4 месяца назад

Wouldn't it be -12 in the beginning instead of +

@cyruschang1904 4 месяца назад

@@GoatedGamer-v7n x^2 - x^3 = 12 => this is given x^3 - x^2 + 12 = 0 => you move x^2 - x^3 from the left of the equation to the right to get 0 = 12 - x^2 + x^3 you rewrite it as 0 = x^3 - x^2 + 12 then x^3 - x^2 + 12 = 0

@GoatedGamer-v7n 4 месяца назад

@@cyruschang1904 didn't notice u switched x^3 and x^2

@cyruschang1904 4 месяца назад

@@GoatedGamer-v7n 🙂

@harrymatabal8448 5 месяцев назад

Excellent. I would have used remainder and factor theorem

@kelvinxyz 4 месяца назад

umm i just guessed x.=-2

@Adam-lx3mt 5 месяцев назад

Nice use of some algebraic identities. Personally, I think it would be more straightforward to solve by guessing the x=-2 solution and then algebraic long division (or comparing coefficients method).

@SpencersAcademy 5 месяцев назад

That's the beauty of mathematics. You can use different approaches and still arrive at the same answer.

@pjaj43 5 месяцев назад

Most of these questions only want integer solutions. x^2 - x^3 = 12 x^2 * (1 - x) = x * x * (1 - x) = 2 * 2 * 3 but also -2 * -2 * 3 by comparison of terms x = -2

@SpencersAcademy 5 месяцев назад

Yea, you're right. But the question did not indicate that x is a real number. That is why the other values of x are also considered.

@МихаилШа-ч6ю 4 месяца назад

Why won’t you use quadratic formula from the start?

@SpencersAcademy 4 месяца назад

This question is not quadratic. It is a 3rd degree polynomial.

@МихаилШа-ч6ю 4 месяца назад

@@SpencersAcademy my bad)

@Смещной_Кощка 4 месяца назад

Thats -2

@superdyus5613 4 месяца назад

It is -2

@Livelovelily-love 4 месяца назад

Seems more like an IQ test. -2

@SpencersAcademy 4 месяца назад

Yeah. When you just focused on the real values.

@Sus9445-d3p 4 месяца назад

I solved that in like 15 seconds. I started at going through possible numbers and started at 2 since 1-1=0, I knew 2^2=4 and 2^3=8 which add to 12. I knew I was on the right track. So i used -2 as x and it worked