a^2-b = b^2-a = 73 a^2-b^2=b-a (a-b)(a+b)=(b-a) (a+b)=(b-a)/(a-b) a+b = -1 eq.1 a=-b-1 a^2-b=73. eq.2 (-b-1)^2-b =73 b^2+2b+1-b=73 b^2+b+1=73 b^2+b-72=0. eq.3 (b+9)(b-8)=0 sol.1 b=-9 sol.2 b=8 from eq.1 a+b=-1 if b=-9 a-9=-1 a=8 if b=8 a+8=-1 a=-9 solutions (a,b)= (8,-9) = (-9,8) VERIFY a^2-b=?73 (8,-9)? 64--9=?73 73=❤73✔️ (-9,8) 81-8=?73 73=❤73✔️ b^2-a has identical results Conclude solutions (a,b)= (8,-9) = (-9,8)

@garrettvanmeter5831

25 күн бұрын

Write as (a,b) = (8,-9) or (a,b) =(-9,8 ). What the solutions as written say is (8,-9) =(-9,8) which is incorrect. Also only One solution is needed Since by symmetry if (8,-9) is a solution then so is (-9,8).

a^2-b=73 b^2-a=73 a^2-b=b^2-a a^2-b^2=b-a (a-b)(a+b)=-(a-b) a-b div 0 a+b=-1 a=-b-1 b^2-a=73 b^2+b+1-73=0 b^2+b-72=0 b=[-1+-rq(1+288)]/2 b=[-1+-17]/2 b1=-9 b2=8 a=-b-1 a1=9-1=8 a2=-8-1=-9

@is7728

27 күн бұрын

Smarter method (gave it a like)

@garrettvanmeter5831

25 күн бұрын

Again, only one solution is needed since you can appeal to symmetry to get the other

@is7728

25 күн бұрын

@@garrettvanmeter5831 Agree

a^2 = 73 + b b^2 = 73 + a the nearest square of an interger that is larger than 73 is 81 by inspection if a equals 9 and b equals -8, the problem is solved.

@彭干

11 күн бұрын

应该是a=-9,b=8或a=8,b=-9吧，你这种解法我们也有类似的，这种解法在中国被称为“瞪眼法”我们写成: 注意到a=-9,b=8是一组解，显然a=8,b=-9是另一组解，证毕。

@ika5666

8 күн бұрын

It took me around 10 sec to find the solution. Glory to Ukraine.

Superb ❤

Hellooooo 😊). A bad solution to an easy problem. After 2:40 we substitute (1) a=b and (2) a=-b-1 in (0) a^2-b-73=0 . We get : (0,1) b^2-b-73=0 , and (0,2) b^2+b-72=0 . Therefore : (3) b1=[ 1-sqrt(293) ]/2 , b2=[1+sqrt(293) ]/2 (4) {thanks to Vietta } : b3=-9 , b4=8 , we substitute (3) in (1) and (4) in (2) . We get the right answer. With respect to, Lidiy

@ashtongreenidge

23 күн бұрын

Recall the condition that a is not equal to b.

Please there is a problem in the factorization

👍🌼

In your solution validation you only plugged values in one of the simultaneous equation. You really need to plug into both of the original simultaneous equations to validate that the solution is valid.

🎉

I did it in my head. but what sort of pen is that? do they do them in other colours?

В первую секунду я подумал, что a=b, и во вторую секунду меня обломали)

a = b = 9.05863

The proposed solution is too much complicated. Below proposed by G is more technical.

I loved this problem!

a = 8, b = -9 or a = -9, b = 8

Задача, на самом деле, очень простая. Вычитаем второе уравнение из первого и после преобразований получаем (a-b)(a+b+1)=0. Отсюда следует a=-1-b (a не равно b по условию задачи). Подставляем полученное выражение для "a" во второе уравнение и получаем b^2+b-72=0. Решаем квадратное уравнение и получаем ответ: 1) b=8, a=-9; 2)b=-9, a=8. Тринадцать минут на такую задачу - очевидный перебор))

@evbdevy352

18 күн бұрын

Я тоже решил именно так,отнял от(1) (2).Получил такое же кв.урав-е.

@evbdevy352

18 күн бұрын

Потратил не более 5 мин.На Олимп.ге тянет

Очень интересно. Спасибо

@user-jk4dn1re9r

21 күн бұрын

Хотя есть и более простые методы решения, но эта игра с формулами мне понравилась.

@learncommunolizer

16 күн бұрын

Your welcome

а=-9, b=8

81-8=73 64+9=73

a=-9 b=8

a=8 b=-9

There are two more real, when a and b are irrational

:))))))))) Jak można tak rozwlekać proste zadanie ?!!! było wstawić a=-b-1 do drugiego równania i wynik gotowy z prostego równania kwadratowego b=-9 ; 8 a=8 ; -9

@YAWTon

24 күн бұрын

The same problem with the same solution was uploaded to YT a short while ago. I think this guy just made a copy of that clip... terribly boring, and bad from a didactic point of view.

а=9 б=-8 !!!

easy to guess the solution by saying what number squared is is slightly greater than 73. result -9 and 8

@salvatorechiocca2375

25 күн бұрын

A

Long winded. It doesn't take 13 mins to solve this!

@YAWTon

24 күн бұрын

You can halve the time by playing the clip at double speed...😊

Всё конечно красиво, но зачем так сильно раскладывать и расписывать очевидные вещи?

I have solved by other way.Plused (1) and (2)

Olympiad problem? I think this is a joke.