China | Can you solve this ? | A Nice Math Olympiad Algebra Problem

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5 ай бұрын

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Пікірлер: 29

@jonnoring7225 5 ай бұрын

Great work! As a college lecturer of mathematics (and also engineer), I always avoid even writing compound numbers, like the 7 1/2 given partway through this video -- compound numbers are ambiguous. Compound numbers should have no place in higher mathematics. In cooking recipes, fine, but not higher math. Also, I always teach the formula that "if a^2 = b, then a = +/- sqrt(b)", where the +/- is applied immediately. This was skipped for one step.

@learncommunolizer 4 ай бұрын

Great tip!

@learncommunolizer 4 ай бұрын

Thank you!

@Hobbitangle 5 ай бұрын

Solving the equation will be greatly simplified after the substitution y= x-9 (y-1)²+y³+(y+1)⁴=2 y²-2y+1+y³+y⁴+4y³+6y²+4y+1=2 y⁴+5y³+6y²+2y=0 The first root is y=0, x=9 y³+5y²+6y+2=0 The next root will be searched from integer dividers of the last coefficient 2, i.e. y=±1,±2, checking only negative ones y=-1,-2 So y=-1 is the next root (x=8) Dividing the polynomial by (y+1) we'll get the quadratic equation y²+4y+2=0 (y+2)²=2 y=-2±√2, x=7±√2 So we've got 4 roots: y=0,-1,-2±√2 x=9,8,7±√2

@rainerzufall42 4 ай бұрын

I would have taken a = x - 9. My intuition is, that it will solve nicely... BTW: First obvious solution is x = 9...

@paulorodriguesbarros7418 5 ай бұрын

A substituição de variáveis é uma forma elegante de resolver essa equação.

@marcgooglegauthier 4 ай бұрын

Bravo.

@learncommunolizer 4 ай бұрын

Thank you very much!

@williammarshal4043 4 ай бұрын

Don't do square root both side like that. If a²= b, a1 = +√b, a2= -√b, because radical √b always positives.

@yapadek3098 6 күн бұрын

He never takes care of this... But he can take 30s to explain why "x-8=y x=y+8)". Mysteries...

@rashtnightamare2701 5 ай бұрын

Cool

@learncommunolizer 4 ай бұрын

Thanks!!👍👍

@jeanrosw 5 ай бұрын

x=9

@kristijanzovko108 5 ай бұрын

Yes

@serkanablak4447 5 ай бұрын

Bu kadar işleme ne gerek var Sonuç iki ise Üç işlemden bir tanesi -1 bir tanesi 0 birtanesi ise +1 olacak üsler zaten çift bu sebebten x=9 çıkar

@sankariraman6453 5 ай бұрын

X=9

@serkanablak4447 5 ай бұрын

İşlem yapmadan kafamdan yaptım x=9

@LooneyKids847 5 ай бұрын

7:43 It's not ±1. It's only +1.

@AkunBelajar-zb9cf 5 ай бұрын

No, it's right. Because we can solve (a² - 1) to (a + 1) * (a - 1). There are 1 and -1, so it's right

@jeevacation 5 ай бұрын

No because you can do -1 * -1 = 1

@LooneyKids847 5 ай бұрын

That is right but when we use roots we only want the positive answer.

@jeevacation 5 ай бұрын

yes but for finding zeroes we go both side of the num line@@LooneyKids847

@rainerzufall42 4 ай бұрын

@@LooneyKids847 sqrt(x) is always non-negative in IR, that's why we write a = +/- sqrt(1), but that's long form of a = -1 v a = 1. This is obviously a polynomial of grade 4, that has exactly 4 solutions (and, see, all of them are real, even positive!)...