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Пікірлер: 168
@irahartoch10752 ай бұрын
There are 6 solutions a =25, b = 24 a = -25, b = -24 a = 25, b = -24 a = -25, b = 24 a = 7, b = 0 a = -7, b= 0 The squares cancel out all the negatives.
@user-nl6jv9ob7z2 ай бұрын
Есть еще решение : а=-7, в=0
@bertthebird23412 ай бұрын
@@user-nl6jv9ob7zThis is solution #6.
@jeffw12672 ай бұрын
This is pretty obviously a Pythagorean triple of the form 7-24-25. I noted that 49 is the square of 7, and the two variables are also squares, so they had to be 25^2 and 24^2.
@davereynolds739Ай бұрын
My question is what did the Math Olympiad have as the correct answer?
@michaelhuppertz6738Ай бұрын
Even more than 6: example (a,b) = (+/-9, sqrt(32)),+/8, sqrt(15),..., without definition D= for (a,b) there are many more, the presenter should limit D to integer only.
@ajeethpandey3 ай бұрын
One equation n two variables it means infinite solutions !
@learncommunolizer3 ай бұрын
Note; {a,b} are elements of Natural numbers which are counting numbers or positive integers, Otherwise we will have many solutions
@lanisilvious70983 ай бұрын
But the question does not say so. And you do not say so in the video. How does one know from looking at question?
@is77283 ай бұрын
Ok thanks for clarifying🙂
@is77283 ай бұрын
And maybe you can pin your comment so that more viewers know this.
@gerar21583 ай бұрын
Los número naturales no incluyen el cero. Son los números enteros.
@HedwigBleicher2 ай бұрын
@@gerar2158El cero es un número natural porque para mucha gente una cuenta bancaria de cero desafortunadamente es natural
@yuki2go3 ай бұрын
a=±7 b=0 a=±25 b=±24
@jaume65bcn3 ай бұрын
Good, our youtuber friend made the tipical mistake of the beginner.
@jeanpaulangevin86183 ай бұрын
@@jaume65bcnon va pas faire de sport on est à l’école de mon père il va me donner une petite cuillère 😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅
@jeanpaulangevin86183 ай бұрын
On va pas faire de sport on est à
@Demon_7033 ай бұрын
it will give the same answer so that he skip this a step(Square cancels the negative)
@giuseppe3y33 ай бұрын
Wrong! Wrong!
@marscience7819Ай бұрын
Umm, 2 unkowns, one equation. That means specific solutions are impossible, you need another equation! Is there an additional specification, like a and b have to be integers?
@peterbyrne63942 ай бұрын
Thank you, very comprehensible explanation.
@XfeeXg3 ай бұрын
Đây là dạng hàm số Y=(X*2+ C)^2 Cho biến số X mọi giá trị sao cho X*2 lớn hơn hoặc bằng C ( nếu C nhỏ hơn không), thì đạt được giá trị tương ứng của Y. Tồn tại vô số cặp nghiệm Cặp nghiệm nguyên dễ nhận ra nhất của đẳng thức a*2 - b*2=49 là a =+ - 7 b =0 ( a phải khác 0)
@pm-os7lz3 ай бұрын
Let a=n and b=n-c, where c is a constant. Thus a^2 - b^2 = 49 can be written as n^2 - (n-c)^2 = 49. Solving for c gives, c = (n^2 - 49)^(1/2) + n. Plug c back into b. Thus, b = -(n^2 - 49)^(1/2). So, if a = n, then b = -((n^2 - 49)^(1/2)). So, a^2 - b^2 = 49 = n^2 - (-(n^2 - 49)^(1/2))^2 = 49, for n >= 7 and n
@yardenvokerol42533 ай бұрын
x²+y²=R² x=b, y=7, R=a therefore, the equation represents the circle b²+7²=a², and has infinitely many solutions in ℝ
@profemarcoresuelve3 ай бұрын
Esta mal su comentario. Si hay infinitas soluciones y estas pertenecen a la grafica de la Hipérbola.
@markdaniel87403 ай бұрын
@@profemarcoresuelvebefore you say that someone is wrong, make sure that you are right. X^2 + y^2 = r^2 will define a circle with radius r that is centered at the origin A hyperbole has more variables to define the focal point
@pm-os7lz3 ай бұрын
Totally makes sense. However, I view the problem not as one trying to find out how many solutions there are, but one that is trying to find specific solutions based on the relationship between a and b.
@profemarcoresuelve3 ай бұрын
@@markdaniel8740 Primero hay que identificar quienes son las variables en el problema. Las variables son a y b, y 49 es la contante ,por consiguiente la igualdad a²-b²=7² que se esta planteando pertenece a la ecuación de la hiperbola que esta centrada en el origen. Lo que ud ha planteado b²+7²=a², no es la ecuación del circulo amigo
@rainerinedinburgh5807Ай бұрын
That's only half correct. The equation x²+y²=r² only represents a circle if x and y are variable and r is the fixed radius. Here you are fixing y=7 (to be more precise, you're fixing y²=7², i.e. |y|=7), and allowing x=b to be one variable, and the radius a to be variable too. For any specific |a|>7, the equation actually represents the four points at which the circle x²+y²=a² intersects the two lines y=7 and y=-7. For |a|
@SALogicsАй бұрын
nice explanation ❤
@lnmukund61523 ай бұрын
In common right angle triangle 7^2= 24+25, consecutive nos in the middle, as per vedic 7^2+24^2=25^2, rest is best known Mukundsir
@zawatsky2 ай бұрын
4:50 для нахождения b проще воспользоваться вторым уравнением системы: ▫a-b=1; ▫-b=1-a; /-1 ▫b=a-1=25-1=24.
@sudhangshubhattacharya4991Ай бұрын
We know that any odd integer = difference between the square values of two consecutive integers
@gheffz3 ай бұрын
Excellent. Thanks.
@learncommunolizer3 ай бұрын
Thank you very much!!
@profemarcoresuelve3 ай бұрын
Incluso \sqrt{59} y \sqrt{10} son soluciones . Por eso se debe plantear bien el problema. Te explico , en realidad hay infinitas soluciones . Las soluciones son todas todos los pares ordenados(x;y) que pertenecen a la grafica de la Hiperbola.
@erdemakca43314 күн бұрын
(a-b).(a+b)=49. The number 49 =49*1. So (a+b)=49 and (a-b)=1. İf we add (a+b) to (a-b) and so add 49 to 1 we can get 2a =50. We can get from this equilibrium that a=25 and b=24
@user-gk1in7on1lАй бұрын
Я решил это задачу за 20 секунд. Мне 56 лет. Работаю сапожником 😅
@elaineassis97433 ай бұрын
🎉🎉🎉
@abasmohammed-zw6pz19 күн бұрын
There are 6 solutions as @purnamishra put it above.so please check again
@alibarka64903 ай бұрын
❤❤
@lnmukund61523 ай бұрын
Mr devdas, It is simple, 49=7^2=24+25 7^2+24^2=25^2, this is applicable 4 all odd no squares Mukundsir
@topquark222 ай бұрын
Much easier way to find a solution in integers: a^2 = b^2 + 7^2 and there's a well-known pythagorean triple, 7^2 + 24^2 = 25^2, so a = 25 and b = 24. Note this doesn't guarantee to have found all solutions.
@johngeier86923 ай бұрын
It took me a few seconds to solve this problem in my head . A =. 25 or -25, B = 24 or -24.
@kurtsalm21552 ай бұрын
I doubt that.
@highworks33983 ай бұрын
Works only if it is Natural numbers
@Ed196013 ай бұрын
Lots and lots of possibilities. The first that comes to mind is ±7 and 0 The next is ±8 and ±sqr15 Next one ±9 and ±sqr32 But also ±sqr50 and ±1 Etc.......... ±25 and ±24 Etc.........
@donsena20133 ай бұрын
I think the presenter wanted to consider only integer values of a and b
@marscience7819Ай бұрын
There are an infinity of solutions. One equation, 2 unknowns.
@davidtorresbenitez41143 ай бұрын
El planteamiento está incompleto no se establece correctamente las condiciones o se están asumiendo condiciones no planteadas
@tomripleyroАй бұрын
shouldn t you add that a and b are positive or at most eqal to 0?
@adityagajjar31183 ай бұрын
Yes he some ans correct.
@neicardenuto935919 күн бұрын
There are inf solutions along the circle of radio 7 ; a2 + b2 = 7^2
@jason-nt6pw7 күн бұрын
피타고라스.정리 7 24 25 역순 플마 25 플마 24
@user-ce9rg8ee9k3 ай бұрын
😅 да ты Энштейн !!! Всю тетрадь исписал, чтобы решить одно маленькое уравнение 😅
@pojuellavid2 ай бұрын
Заграница всегда так решает, для дебилов.
@purnamishra3 ай бұрын
This is not correct math. You should have shared your assumptions at the beginning. You are assumung both a and b to be >= 0 and are integers. Otherwise, in this case it is one equation with two variables. So there are multiple values for both a and b. If you assume a to be dependent and b is independent then for all values of a (both positive and negative), there is a value for b. Please each correct math.
@humbertorodriguezperez12143 ай бұрын
He is assuming that b >= 0 and a > b (or else a^2 - b^2 =< 0), as well as that both are integers. And right, he should have said he was assuming these premises before starting solving the problem
@dnickaroo35743 ай бұрын
Why take so long to derive such a simple result, after the above assumptions are given?
@pas62953 ай бұрын
கரேக்ட்
@shushantadebnath56303 ай бұрын
This is not the correct solution for the math.
@bertthebird23412 ай бұрын
@@pas6295What language is this?
@user-ee7nw2rx9s3 ай бұрын
Почему не все ответы? Если а= - 7, b=0 это одно из решений, которого нет в ответе, также а=-25, b=-24, тоже будут решение Всего существуют 6 решений которые не указаны как решение
@momus12343 ай бұрын
Only b>0, Plus a =0, b =-7
@cachotrelles47153 ай бұрын
Sensacional explicación 👏👏👏👌👌
@mtbbk3 ай бұрын
Ja
@mathewjohn81262 ай бұрын
Thanks 😊
@learncommunolizer2 ай бұрын
You're welcome! Thank you very much!
@kurthaas61863 ай бұрын
625 - 576 = 49. 25^2 = 625; 24^2 = 576. Die Frage ist nur, welche 2 aufeinanderfolgenden Zahlen 49 ergeben. Die Berechnung funktioniert geht so auf, weil die Exponenten dieselben sind.
@gerar21583 ай бұрын
¿Cómo salen las soluciones?. Si se hace a=bk (con “k”constante). De ahí, operando algebraicamente se desprende que b=(7*((k+1)(k-1))^1/2)/(k+1)(k-1). En consecuencia, para cada valor de “k" existirá un par ordenado (a,b) que es solución. para A^2-b^2=49
@TexasHoosier31183 ай бұрын
7, 24,25 pythagorean triplet
@gerar21583 ай бұрын
Para la reflexión de los amigos. ¿Son esas las únicas soluciones?. Por ejemplo: a=14/3(3)^1/2; b=7/3(3)^1/2, ¿es solución?.Si es correcto, ergo, hay infinitas soluciones. salvo que se pidan solo soluciones en el campo de los Z (números enteros) exclusivamente, cosa que no se aclara.
@MaxVig201415 күн бұрын
Also 7 and 0 : (7+0)(7-0)=49
@veenakundra77524 күн бұрын
It is not the method to solve the equation these are only permutation combination.to find the value of two variables there must be two equations
@venkatesank38412 ай бұрын
Two more answers. a+b = -7. a-b = -7. In this case a = -7; b = 0.
@henk-ottolimburg79472 ай бұрын
The difference of 2 consecutive squares is an odd number. a and b differ 1 it's 49/2, so that leads to 24-25 Are there any other solutions? a and b differ 2 is no good, the squares differ by two odd numbers, so that's even. could they differ 3? That would be (x-2)+ x + (x+2), average x, 49 is not divisable by 3. Neigther is it divisable by 5. But it is divisable by 7, so (x-7)+(x-5) etc. average x=7 1+3+5+7+9+11+13=49, so 0 and 7. Written down like this it seems complicated, but take the first and fourth line and write that in a table
@gonzalofernandezramon695420 күн бұрын
I haven't heard that a and b should be integer numbers.
@user-bt9hv7ce4e3 ай бұрын
전제 조건이 자연수?
@farmerjohn61923 ай бұрын
How about a 7, 24, 25 common right angle triangle
@jeffw12672 ай бұрын
I spotted that in a fraction of a second, after noting that 49 is 7^2 and that both the variables are also squared. It's recommended that students memorize the smallest Pythagorean triples for college entrance exams. These are 3-4-5, 5-12-13, 8-15-17, and 7-24-25.
@SankaranArumugam-xl1hc2 ай бұрын
A 8 b 5
@johnlay3040Ай бұрын
The easiest solution is a=7 and b=0
@claudiacampos590115 күн бұрын
( a + b) (a- b)=7
@ziyadxanaliyev390620 күн бұрын
a+ b = 7 ; a- b = 7 ;a +b = a - b , 2b = 0 b = 0 ; a + b = 7 , a - b = 7 ответ : а = 7 , b = 0 .
@abdellahlemjidi8141Ай бұрын
-7._7=49
@Bill-uo6cm3 ай бұрын
7, 0
@romanaskarov10192 ай бұрын
Я в уме без решения нашел корни. И так ясно a=7, b=0.
@zbigniewdubrawa71763 ай бұрын
A=b+1 a=25;b=24
@DimaCharapko23 күн бұрын
Do have maht adulation besayd school?
@thichhochoi76619 күн бұрын
49 = 24.5 x 2? Who said a, b must be integer?
@antonkamolov2385Ай бұрын
How to unsee that. And this channel. Omg.
@dardoburgos3179Ай бұрын
a= 24, b=23.
@rumetiskl65603 ай бұрын
7 24 25 pysagor
@xpthewindowsguygaming3 ай бұрын
Thêm điều kiện của bái toán a and b phải là số nguyên
@professorsargeanthikesclim92932 ай бұрын
Apparently nonnegative, in fact.
@is77283 ай бұрын
Did you say that a and b are natural numbers?
@mtbbk3 ай бұрын
Yes
@is77283 ай бұрын
@@mtbbk If so, then at what time?
@mtbbk3 ай бұрын
@@is7728 Oh he did not say but from the answer we can say yes
@is77283 ай бұрын
@@mtbbk I understand but there are indeed infinitely many solutions if the question isn't well-written
@jessewallis65893 ай бұрын
What are some other solutions?
@user-bk6gx7sg3j3 ай бұрын
Two unknowns, one equation. Cannot be done. The answer will be speculative. Clearly, a or b is 7, at the same time the other must be 0. The since we have two unknowns in one equation, we have no way of binding the solutions to the variables. Everything else done or said here is nothing but meaningless mathematical gymnastics
@sr642410 күн бұрын
This is an Olympiad problem. So why weren’t negative and imaginary solutions considered?
@tanklar13 ай бұрын
a=7 b=0 , a is not -7 ,it is imposible, I solved the problem
@pas62953 ай бұрын
+8ஆர்-8அண்ட் +5ஆர் -5
@awwa20043 ай бұрын
2а=50. Из этого СРАЗУ получается а=25. Зачем сначала все делить на 2, потом сокращать 2, и получать 25. Для кого вы читаете математику? Тот кто смотрит это, тот уже кое что смыслит в математике. Эти подробности раздражают. Смотреть не хочется. Это какой-то незыблемый метод и без него сам лектор не может?
@michaelsteinberg13 ай бұрын
There are an infinite number of solutions. I'm not satisfied with this approach.
@user-dv8gv3hu4t2 ай бұрын
Solution by insight 64-25=49 a=8, b=5
@HedwigBleicher2 ай бұрын
64-25=39.
@mokaralavenkataramana77413 ай бұрын
Use Pythagoras
@zlisiecki2 ай бұрын
a = 7, b = 0
@WB8BRA3 ай бұрын
a=56 b=7 a-b = 49 Ok, so I guessed ... it was sure as hell easier that the above. Ok, I am not a math person, but am I wrong???
@HedwigBleicher2 ай бұрын
Yes , you are right that you are wrong. It is a^2-b^2=49=7^2.
@professorsargeanthikesclim92932 ай бұрын
Don't ignore the squaring and don't only look for one solution if not specified.
@lanisilvious70983 ай бұрын
OK so. . .idiot question. Why only use the positive factors (1 × 49)(49 × 1)(7 × 7)? (-1 × -49) = 49. (-49 × -1) = 49. (-7 × -7) = 49 For example, using -1 and -49 (-1 > -49) a + b = -1 a - b = -49 2a = -50 a= -25 b = -24 Check: a^2 - b^2 = 49 -25 can be squared (-25)^2 = 625 -24 can be squared (-24)^2 = 576 625-576 = 49 Try -7 and -7 a + b = -7 a - b = -7 2a = -14 a = -7 b = 0 Check a^2 - b^2 = 49 (-7)^2 - 0^2 = 49 -7 can be squared (-7)^2 = 49 So a^2 is 49 if a = -7 49 - 0^2 = 0 0 squared is 0 So b squared = 0 49 - 0 = 49 So i got (a,b) = (7, 0) or (25, 24) or (-7, 0) or (-25, -24). So. . .why are negative factors not factors? Where is the error in my math?
@sadhumetta67703 ай бұрын
I was going to ask the same question as well.
@saikrishnavedula83303 ай бұрын
Only person could solve is Modi.
@entertainmentzone68383 ай бұрын
a=± 7 & b= 0
@tanklar13 ай бұрын
a cannot be -7. a=7 b=0 I solved the problem
@entertainmentzone68383 ай бұрын
@@tanklar1 why?
@tanklar13 ай бұрын
@@entertainmentzone6838 because a+b=a-b=7
@tanklar13 ай бұрын
@@entertainmentzone6838 a-b=a+b=7
@entertainmentzone68383 ай бұрын
@@tanklar1 a+b=-7 & a-b=-7 also
@EA-ig3ndАй бұрын
It ist not correct. Pythagoras: a²+b2=c2 Here: c²+b²=a² 7²+b²=a² When you change the value from b so you change automatically the value from a So you have endless possibilities
@07spartak65Ай бұрын
Можно решить в уме. Спасибо образованию СССР. Мне 60,решила гораздо быстрее.