France Math Olympiad | How to Solve ab+c=2020, a+bc=2021 | You Should Know This Trick | Algebra

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How to solve ab+c=2020, a+bc=2021
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31 май 2024

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Комментарии : 14

@nickcallil6971 Месяц назад

Need to state the condition a,b,c are integers

@SpencersAcademy Месяц назад

Yeah, you're right.

@SpencersAcademy 26 дней назад

@@irvingrabin thanks for the info

@AIUskow 17 дней назад

I also had an immediate question: why can't (1-b) equal 2 and (a-c) = 1/2? But, in integers everything is solved correctly.

@harrymatabal8448 Месяц назад

Excellent

@SpencersAcademy Месяц назад

Thank you! Cheers!

@YaxunKe 28 дней назад

why is it not 0,5*2 (or something) it is also equal to 1 right?

@RealQuInnMallory Месяц назад

(abc➖2anc+2) (abc➖3abc+2)

@EnochAkintayo 29 дней назад

You didn't say if the condition for the solutions is that they must be integers. I can think of countless products that give 1 as answer.

@SpencersAcademy 29 дней назад

They a, b, and c are all integers

@rob876 Месяц назад

Integer solutions: a - c - b(a - c) = 1 (a - c)(1 - b) = 1 a - c = 1 and b = 0 => c = 2020, a = 2021 or a - c = -1 and b = 2 => 2a + a + 1 = 2020 => 3a = 2019 => a = 673, c = 674 (a, b, c) = (2021, 0, 2020) or (673, 2, 674)

@SpencersAcademy Месяц назад

Excellent.

@giannaleoci2328 29 дней назад

ab+c=2020 a+bc=2021 a-ab+bc-c=1 (a-c)-b(a-c)=1 (a-c)(1-b)=1 1) a-c=1 1-b=1 b=0 a=c+1 c=2020 a=2021 2) a-c=-1 ;1-b=-1 b=2 a=c-1 ab+c=2020 (c-1)2+c=2020 2c-2+c=2020 3c=2022 c=674 a=673 b=-1

@SpencersAcademy 28 дней назад

Excellent. I love this. It is neat.