Germany - Math Olympiad Question | The BEST Trick

Подписаться 16 тыс.

Просмотров 15 тыс.

50% 1

You should know this approach. Solution
What do you think about this problem? Don't forget to like and subscribe to my channel for more helpful math tricks. Thanks For Watching!
Check out my latest video (Can You Pass Harvard's Entrance Exam?): • Can You Pass Harvard's...
If you're reading this ❤️. Thank You!
Hello My Friend ! Welcome to my channel. I really appreciate it!
‪@higher_mathematics‬
#maths #math

Опубликовано:

5 июл 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 32

@ManojkantSamal 10 дней назад

a=4, b=2 As per question a+2ab+b=22 Multiply 2 on both the sides3 2a+4ab+2b=44 Add 1 on both the sides3 2a+4ab+2b+1=44+1=45 2a(1+2b)+1(1+2b)=45 (1+2b)(2a+1)=9×5 or 15×3 Let's take 9×5 So, (1+2b)(2a+1)=9×5 So, 1+2b=9 and2 2a+1=5 2b=9-1 and 2a=5_1 2b=8 and 2a =4 b=4 and a=2( also vice versa)

@prime423 16 дней назад

The key is the solutions are integers. Simply solve for a in terms of b.No fancy manipulation necessary. Always look for simple solutions first. In addition,thats applicable to all linear Diophantine equations.

@roberthayter157 16 дней назад

Excellent, as usual. What I learn is that I need to learn to be more creative. 😊

@yogamulyadi2046 2 дня назад

(2a+1)(2b+1)=45 (a;b)={(1;7),(7;1),(2;4),(4;2)}

@giannaleoci2328 12 дней назад

Eccellente soluzione!

@DebdasBandyopadhyay-yq5jg 16 дней назад

Is it called integer Solution?

@giuliofalco9816 16 дней назад

I solved in this way: a + 2ab + b = 22 -> b(2a +1) = 22 - a -> b = (22 - a) / (2a +1). b must be integer so I can compute rhis table a | 2a +1 | 22 -a -------------------------------- 1 3 21 x (22-a divide 2a +1) b=7 2 5 20 x b= 4 3 7 19 4 9 18 x the same solutions switched 5 11 17 6 13 16 7 15 15 x 8 17 14 9 19 13 10 21 12

@harrymatabal8448 16 дней назад

Good work from you and Mr Giulio. Thanks

@keithwillenson8314 4 дня назад

2a + 1 >= 3 is not true if a (or b) = 0, you missed the 1, 45 pair and 45, 1 pair or (0, 22) and (22, 0) as long as your solution is only non-negative integers

@tombufford136 16 дней назад

At a quick glance if a = 4 and b = 2 then 4+16 + 2 = 22. This gives two solutions: a = 4 and b = 2. a = 2 and b = 4.

@LinhTran-om6qh 16 дней назад

How did you come up with tricks like multiplying both sides with 2 and then adding 1 to both sides? I mean, it seemed so random what you did and yet effective. Is there any signal of when to use such tricks and which tricks to use?

@neon1300 16 дней назад

Same question here.

@immersivalgames2696 16 дней назад

What I think he did is that he factored a+2ab and got a(1+2b) or a(2b+1) and since there is still one b left over he matched the factor by multiplying both sides by 2 to get the 2b and added 1 to finally match the factor so he can get 2a(2b+1) + 1(2b+1) = 45 And simplified it to (2b+1)(2a+1)=45. This can also be done to 2ab + b but for the video it was done as a + 2ab.

@Cagouille79 16 дней назад

a(1+2b)+b=22 a=(22-b)/(1+2b) For each value of b you have a value for a except if 1+2b=0 (if b=-1/2) So, number of solutions = Infinite. Isn't it ?

@SubhroMandal-r8k 15 дней назад

Bro! Only positive integers are asked.

@TheFrewah 10 дней назад

You could do a(1+2b) +b =22. And now you see you want the single b to be 2b+1 so you multiply by 2 and add 1 and then you can factorise.

@bookert2373 16 дней назад

a+b = 22-2ab, so a+b is divisible by 2. Therefore, both are even or both odd. a+b positive, so 2ab < 22 and ab < 11. There are very few positive pairs of (a,b) to test that are both odd or both even that and satisfy ab

@user-nr6tt5he7g 16 дней назад

Continuing your reasoning. Let a≡a' and b≡b' (mod 4), where 0

@gogo201158 12 дней назад

This is too complicated,it is because a and b are positive integer,just try a equal to 1 to 6, then you can find all answers

@EduardoDuvane-mc7dm 16 дней назад

It's big a deal👏🏻👏🏻👏🏻 I have a math olympiad question, can I send it?

@maryjay7833 14 дней назад

Please send it here, we will either help or learn something😊

@olegg9726 8 дней назад

a=2 and b=4...Just be common sense!

@user-ul3ms1og2f 15 дней назад

a = 1 and b = 7 ?

@Mofiac 15 дней назад

And 22, 0. His answers don't work in the original equation .

@quantumbuddha777 14 дней назад

@@Mofiaczero is not a positive integer

@Mofiac 15 дней назад

(1,7), (7,1), (0, 22), (22,0) are the only solutions. Your answers don't work with the original equation.

@maryjay7833 14 дней назад

Sorry my friend , but you are wrong, a and b must be positive. He solved it nicely

@nikolayguzman331 16 дней назад

There are more answers: a=22 b=0 and simetrical a=0 b=22 The solve idea is very nice and creative.

@johnlv12 16 дней назад

a and b must be positive

@harrymatabal8448 16 дней назад

Was your fourth step necessary. Wasting our time

@richardslater677 13 дней назад

You have used totally unexplained steps such as multiplying by two and adding one to both sides. These steps seem picked out of the air with no logical reasoning. You do this a lot on your channel and I’ve commented as such in precious videos. It would be very useful for me if you could explain the reasons why you choose each step please.