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-nl6jv9ob7z

2 ай бұрын

Есть еще решение : а=-7, в=0

@bertthebird2341

Ай бұрын

​@@user-nl6jv9ob7zThis is solution #6.

@jeffw1267

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.

@davereynolds739

Ай бұрын

My question is what did the Math Olympiad have as the correct answer?

@michaelhuppertz6738

Ай 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.

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

@profemarcoresuelve

3 ай бұрын

Esta mal su comentario. Si hay infinitas soluciones y estas pertenecen a la grafica de la Hipérbola.

@markdaniel8740

3 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-os7lz

3 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.

@profemarcoresuelve

3 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

@rainerinedinburgh5807

Ай 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|

a=±7 b=0 a=±25 b=±24

@jaume65bcn

3 ай бұрын

Good, our youtuber friend made the tipical mistake of the beginner.

@jeanpaulangevin8618

3 ай бұрын

@@jaume65bcnon va pas faire de sport on est à l’école de mon père il va me donner une petite cuillère 😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅😅

@jeanpaulangevin8618

3 ай бұрын

On va pas faire de sport on est à

@Demon_703

3 ай бұрын

it will give the same answer so that he skip this a step(Square cancels the negative)

@giuseppe3y3

3 ай бұрын

Wrong! Wrong!

Thank you, very comprehensible explanation.

Note; {a,b} are elements of Natural numbers which are counting numbers or positive integers, Otherwise we will have many solutions

@lanisilvious7098

3 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?

@is7728

3 ай бұрын

Ok thanks for clarifying🙂

@is7728

3 ай бұрын

And maybe you can pin your comment so that more viewers know this.

@gerar2158

3 ай бұрын

Los número naturales no incluyen el cero. Son los números enteros.

@HedwigBleicher

Ай бұрын

​@@gerar2158El cero es un número natural porque para mucha gente una cuenta bancaria de cero desafortunadamente es natural

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

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)

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

We know that any odd integer = difference between the square values of two consecutive integers

nice explanation ❤

4:50 для нахождения b проще воспользоваться вторым уравнением системы: ▫a-b=1; ▫-b=1-a; /-1 ▫b=a-1=25-1=24.

Excellent. Thanks.

@learncommunolizer

3 ай бұрын

Thank you very much!!

One equation n two variables it means infinite solutions !

El planteamiento está incompleto no se establece correctamente las condiciones o se están asumiendo condiciones no planteadas

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.........

@donsena2013

3 ай бұрын

I think the presenter wanted to consider only integer values of a and b

@marscience7819

Ай бұрын

There are an infinity of solutions. One equation, 2 unknowns.

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.

Sensacional explicación 👏👏👏👌👌

@mtbbk

3 ай бұрын

Ja

😅 да ты Энштейн !!! Всю тетрадь исписал, чтобы решить одно маленькое уравнение 😅

@pojuellavid

2 ай бұрын

Заграница всегда так решает, для дебилов.

Я решил это задачу за 20 секунд. Мне 56 лет. Работаю сапожником 😅

It took me a few seconds to solve this problem in my head . A =. 25 or -25, B = 24 or -24.

@kurtsalm2155

2 ай бұрын

I doubt that.

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

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.

🎉🎉🎉

❤❤

Works only if it is Natural numbers

¿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

There are 6 solutions as @purnamishra put it above.so please check again

How about a 7, 24, 25 common right angle triangle

@jeffw1267

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.

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.

@humbertorodriguezperez1214

3 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

@dnickaroo3574

3 ай бұрын

Why take so long to derive such a simple result, after the above assumptions are given?

@pas6295

3 ай бұрын

கரேக்ட்

@shushantadebnath5630

2 ай бұрын

This is not the correct solution for the math.

@bertthebird2341

Ай бұрын

​@@pas6295What language is this?

There are inf solutions along the circle of radio 7 ; a2 + b2 = 7^2

전제 조건이 자연수?

Thanks 😊

@learncommunolizer

Ай бұрын

You're welcome! Thank you very much!

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

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?

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

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.

Did you say that a and b are natural numbers?

@mtbbk

3 ай бұрын

Yes

@is7728

3 ай бұрын

​@@mtbbk If so, then at what time?

@mtbbk

3 ай бұрын

@@is7728 Oh he did not say but from the answer we can say yes

@is7728

3 ай бұрын

@@mtbbk I understand but there are indeed infinitely many solutions if the question isn't well-written

@jessewallis6589

3 ай бұрын

What are some other solutions?

Yes he some ans correct.

Only b>0, Plus a =0, b =-7

7, 24,25 pythagorean triplet

shouldn t you add that a and b are positive or at most eqal to 0?

I haven't heard that a and b should be integer numbers.

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.

Do have maht adulation besayd school?

How to unsee that. And this channel. Omg.

Two more answers. a+b = -7. a-b = -7. In this case a = -7; b = 0.

7, 0

Thêm điều kiện của bái toán a and b phải là số nguyên

@professorsargeanthikesclim9293

Ай бұрын

Apparently nonnegative, in fact.

कैसे संभव है यदि a+b बड़ा होगा a-b से तो a+b=7 and a - b=7 not possiable

@heinrich.hitzinger

2 ай бұрын

a+b>=a-b means a+b>a-b or a+b=a-b

A 8 b 5

Also 7 and 0 : (7+0)(7-0)=49

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???

@HedwigBleicher

Ай бұрын

Yes , you are right that you are wrong. It is a^2-b^2=49=7^2.

@professorsargeanthikesclim9293

Ай бұрын

Don't ignore the squaring and don't only look for one solution if not specified.

Я в уме без решения нашел корни. И так ясно a=7, b=0.

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 .

-7._7=49

A=b+1 a=25;b=24

Use Pythagoras

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

49 = 24.5 x 2? Who said a, b must be integer?

7 24 25 pysagor

a=7 b=0 , a is not -7 ,it is imposible, I solved the problem

( a + b) (a- b)=7

There are an infinite number of solutions. I'm not satisfied with this approach.

The easiest solution is a=7 and b=0

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?

a=± 7 & b= 0

@tanklar1

3 ай бұрын

a cannot be -7. a=7 b=0 I solved the problem

@entertainmentzone6838

3 ай бұрын

@@tanklar1 why?

@tanklar1

3 ай бұрын

@@entertainmentzone6838 because a+b=a-b=7

@tanklar1

3 ай бұрын

@@entertainmentzone6838 a-b=a+b=7

@entertainmentzone6838

3 ай бұрын

@@tanklar1 a+b=-7 & a-b=-7 also

8*8=64-5*5=25

@HedwigBleicher

Ай бұрын

64-25=64-20-5=44-5=39≠49

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?

@sadhumetta6770

3 ай бұрын

I was going to ask the same question as well.

+8ஆர்-8அண்ட் +5ஆர் -5

Solution by insight 64-25=49 a=8, b=5

@HedwigBleicher

Ай бұрын

64-25=39.

Forty nine❌ Foty nin✅

bro forgor plus or minus

a= 24, b=23.

A=25 B=34

@user-ce9rg8ee9k

2 ай бұрын

Ага = 59 😅

Only person could solve is Modi.

a = 7, b = 0

It's not completely

2. 2 a. - b. =. 49. , a > b 49+1. =. 50 ÷ 2 =25 2 2 25 > 24 25. 24. = 49. Verify 625 - 576. =. 49 So simple..... I follow this short cut method Shortcut square root method.. 15 x 15. = 225+ 15+15+1. =. 31 16 x 16. =. 256+ 16+16+1. =. 33 17x17. =. 289+ 17+17+1 =. 35 18x18. =. 324+ 18+18-1. =. 37 19x19. =. 361+ 19+19+1 =. 39 20x20. =. 400+ 20+20+1.=. 41 21x21. 441+ 21+21+1. =. 43 22x22. =. 484+ 22+22+1.=. 45 23x23. =. 529+ 23+23+1. = 47 24x24. = 576+ 24+24+1. =. 49 25x25. =. 625+ 25+25+1. =. 51 26x26. =. 676+ 26+26+1. =. 53 27x27. =. 729+ 27+27+1. =. 55 28x28. =. 784+ 28+28+1. = 57 29x29. =. 841+ 29+29+1. =. 59 30x30 =. 900+ 30+30+1. =. 61 31x31. =. 961+ 31+31+1. =. 63 32x32. = 1024+ 32+32+1. =. 65 33x33. =. 1089+ 33+33+1. 67 34x34. =. 1156+ 34+34+1. 69 35x35. =. 1225+ 35+35-1. =. 71 36x36. =. 1296+ 36+36+1. =. 73 37x37. =. 1369+ 37+37+1. =. 75 38x38. =. 1444+ 38+38+1 =. 77 39x39. 1521+ 39+39-1. =. 79 40x40. 1600 If you go on adding the two multiplying number plus 1, you will frame square numbers of subsequent numbers easily

Your not checking the solution at the end. You can trust the maths. Your really checking you didn’t make a mistake

Now solve it using calculus.

@Mal1234567

Ай бұрын

All those who think calculus can't be used to solve this, raise their hands.

Это если a и b больше 0

@professorsargeanthikesclim9293

Ай бұрын

And integers.

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

(25;24)(7;0)(-25;-24)(-7;0)

Cuidado... Estas llegando a unas conclusiones matemáticas que no tienen logica

Можно решить в уме. Спасибо образованию СССР. Мне 60,решила гораздо быстрее.

Uygun bir soru degil, hemde kolay

Бред.

If you have memorised squares, you know the answer.

@robertloveless4938

3 ай бұрын

That's how I did it. Took about 15 seconds. Just gobup the number line by odd numbers, keep track of how many numbers used. EASY PEASY.

@Uttrediay

3 ай бұрын

Not to brag, but I used a fraction of a second to recall that the difference between 25 and 24 squared is 49 (625 minus 576).

@alfredofettuccine9425

2 ай бұрын

No need to memorize anything: any odd number 2n+1 is the difference between 2 consecutive numbers n and n+1 squared…

-7 -25 -24 are all forgotten in your answers THUMBS DOWN

This is mediocre way of doing math. And the fellow thinks it is Olympiad level maths.😅

No solution. One equation two unknown

@professorsargeanthikesclim9293

Ай бұрын

Incorrect. Infinitely many, unless specified to be integers or nonnegative integers.

This is wrong

a^2 - b^2 = 7^2 => a=7, b=0. Not perfect hindu logic

This is very wrong. Also too many steps. Here is the right answer A=4 B= 3 4×4 =16 3×3= 9 . 16- 9=7.

Just no. Stop.

Very poor skill of teaching.

😮много лишней информации, бык❗

答え　a=7 b=0