More simply: a is one of dividers of 3 (1,3), and b is one of dividers of 4 (1,2,4), is only 2 solutions for equality 3/a+4/b=5 : (a=1, b=2) and (a=3 , b=1)
Вот точно такое же решение хотела написа́ть. Типичное поставление подходящих чисел. This is exactly the same solution I wanted to write. A typical placement of suitable numbers.
a = 3 and b = 1 a = 1 and b = 2 a = 9/11 and b = 3 a = 12/16 and b = 4 a = 15/21 and b = 5 a = 18/26 and b = 6 a = 21/31 and b = 7 a = 24/36 and b = 8 a = 27/41 and b = 9 etc....
too complicated. rearrange the numbers to solve for A, then substitute that formula into "A" in the original equation, solve for b, which leads to solving for a.
Yes, Math can be very complicated, it is clear from this video. But it can also be simple, I saw from the first 5-6 seconds that the answers are 3, 1 or 1 and 2... If you want to complicate things and make people to hate Mathematics, then do the demonstration above!
@@nguyminh721 That may be true, but the initial data does not specify what kind of numbers represent the solutions for a and b. And then, the beauty of mathematics could be also in its simplicity, as someone correctly writes in these comments.
Задание не корректное ! При двух неизвестных должно быть второе уравгение !( чтобы был один точный ответ ) . Иначе только методом подбора и это не верно , т.к. решений может быть множество !
i do not agree. The suggested "substitutions" in all 4 cases are like AxB=CxD and from here is derived a new equality --- A=C and B=D, which is wrong! Let's substitute few numbers --- 2x10=4x5 - neither 2 is equal to 4, nor 10 to 5! And anything after that does not make any mathematical sense.
The solution is far too long. Trivial obvious manipulations presented in a long-winded manner make it extremely unpleasant to watch. Teaching math is clearly not your thing. Here is how it is done. If a>3, then 3/a+4/b
It seems that knowing the solutions which are obvious here you invent a backward path as complicated as possible. What bothers me is that you risk making young people sick of mathematics.
@@LeLibossien You miss the point: I have shown that there are no other solutions. My one-line proof is the exact opposite of the ``complicated". Incidentally: do not mix logic arguments with emotional concerns about what other people will like or dislike. The beaty of math is that any considerations other than the truth, utility, and the rigor of its statement are irrelevant.
@@xgx899 Please do not misunderstand me. My intention was not to denigrate your algebraic manipulation skills but to encourage you to show a path that any serious student can take. Here for example: 3/a +4/b=5 everyone comes easily to: 3b+4a-5ab=0 many will remark that it is a partial development of (a-3/5)*(-5b-4) only 12/5 is missing so: (a-3/5)*(-5b-4)-12/5 =0 finally: (5a-3)*(5b-4)=12 The rest you have it. Beauty is also in simplicity.
Очень замороченный способ решения!!!!!!! Ужас какой-то. Даже умному взрослому с высшим образованием, человеку.. и то.. слишком уж замороченный. А ребенку!!!! Ученику??????
Because a and b are positive integrrs, the only choices are a=1 or a=3.
If a=1, then 4/b = 5 - 3/1 so b=2
If a=3, then 4/b = 5 - 3/3 so b=1
More simply: a is one of dividers of 3 (1,3), and b is one of dividers of 4 (1,2,4), is only 2 solutions for equality 3/a+4/b=5 : (a=1, b=2) and (a=3 , b=1)
Очень легкий пример.a=1,b=2
Есть второй вариант: а=3,b=1
ответы очевидны с первого взгляда и незачем такой огород городить
5=3+2
3/1=3
4/2=2
a=1, b=2
A=3, b=1; or a=1, b=2 whichever there’s lots more solutions no fancy math needed
Indeed. It is hard to believe that this is a math olympiad problem.
v2.
5=4+1
3/3=1
4/1=4
a=3. b=1
3/1 plus 4/2 = 5 ; 3 plus 2 = 5; a= 1, b= 2 😍 nobody has to calculate
Вот точно такое же решение хотела написа́ть. Типичное поставление подходящих чисел.
This is exactly the same solution I wanted to write. A typical placement of suitable numbers.
видно сразу ответ из заставки
a = 3 and b = 1
a = 1 and b = 2
a = 9/11 and b = 3
a = 12/16 and b = 4
a = 15/21 and b = 5
a = 18/26 and b = 6
a = 21/31 and b = 7
a = 24/36 and b = 8
a = 27/41 and b = 9
etc....
Bello ejercicio matemático. Pero la música también lo es. Puedes indicar el nombre del tema y su intérprete
Master. why do you prefer unnecessarily complicated method?
a=3 b=1
a=1. b=2
1, 2
b=4/5 + (1/5)(12/(5a-3))
Therefore: 12/(5a-3) can be 1 or 6 only
Thus a can be 3 or 1 only
Hence: (1,2) & (3, 1) are only positive integral solutions.
Нет, А может быть и отрицательным числом, например, -1, тогда В=0.5
Question says a, b€ Z+@@ИринаКомарова-у7ъ
1 + 4 = 5
сколько будет равен Х, если 2х+6=12
И ты такой давай считать через графики и дискриминант, интервалы, корни логорифмы...
A is one and b is two.
Why add 12/5? How did You "get that idea"?
He used equivalency principal to factorise Left hand side
He wants to factorise (b-4/5).
He had already 3b .
3(b-4/5)=3b-12/5
too complicated. rearrange the numbers to solve for A, then substitute that formula into "A" in the original equation, solve for b, which leads to solving for a.
Yes, Math can be very complicated, it is clear from this video. But it can also be simple, I saw from the first 5-6 seconds that the answers are 3, 1 or 1 and 2... If you want to complicate things and make people to hate Mathematics, then do the demonstration above!
Maybe we should do like that to find out if there are some more answers that satisfy the conditions !
@@nguyminh721 That may be true, but the initial data does not specify what kind of numbers represent the solutions for a and b. And then, the beauty of mathematics could be also in its simplicity, as someone correctly writes in these comments.
a=1 ; b =2
Задание не корректное ! При двух неизвестных должно быть второе уравгение !( чтобы был один точный ответ ) . Иначе только методом подбора и это не верно , т.к. решений может быть множество !
не пойму как у меня получилось а=1.2 в=1.6
a egal 3:b egal 1 simplu
К чему такая сложность? За минуту ,если учесть условие .,что а и в целое положительное.
i do not agree. The suggested "substitutions" in all 4 cases are like AxB=CxD and from here is derived a new equality --- A=C and B=D, which is wrong! Let's substitute few numbers --- 2x10=4x5 - neither 2 is equal to 4, nor 10 to 5! And anything after that does not make any mathematical sense.
You don't have to recopy the line every time. Anyone who knows where you got the 12/5 at 2:20 will be able to do simple arithmetic in their heads.
Это же элементарно.....
Obviously 5 = 3 + 2 so a = 1, b= 2
3. 1. 1. 2
What if a was 3 and b was 1 ?
А можно сразу?.
а=3 ;b=1
Infinite answers as the question does not specify what a and b number types are.
Ужас какой то. Я в уме сосчитала, что А равно 1,а б равно 2.
B=2 y A= 1
А=3, В=1 ????? 😂
Nu se poate simplifica rezolvarea?
12=24*0.5, 48*0.25...?
а=1 в=2 !!!
а равно 3, б равно 1
The solution is far too long. Trivial obvious manipulations presented in a long-winded manner make it extremely unpleasant to watch.
Teaching math is clearly not your thing.
Here is how it is done. If a>3, then 3/a+4/b
It seems that knowing the solutions which are obvious here you invent a backward path as complicated as possible. What bothers me is that you risk making young people sick of mathematics.
@@LeLibossien You miss the point: I have shown that there are no other solutions. My one-line proof is the exact opposite of the ``complicated".
Incidentally: do not mix logic arguments with emotional concerns about what other people will like or dislike. The beaty of math is that any considerations other than the truth, utility, and the rigor of its statement are irrelevant.
I agree that.
@@LeLibossienWho are you writing to? You should indicate that.
@@xgx899 Please do not misunderstand me. My intention was not to denigrate your algebraic manipulation skills but to encourage you to show a path that any serious student can take. Here for example: 3/a +4/b=5
everyone comes easily to: 3b+4a-5ab=0
many will remark that it is a partial development of (a-3/5)*(-5b-4) only 12/5 is missing
so: (a-3/5)*(-5b-4)-12/5 =0
finally: (5a-3)*(5b-4)=12
The rest you have it.
Beauty is also in simplicity.
Очень замороченный способ решения!!!!!!! Ужас какой-то.
Даже умному взрослому с высшим образованием, человеку.. и то.. слишком уж замороченный.
А ребенку!!!! Ученику??????
а = 3; b = 1