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)

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

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.

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

Superb ❤

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.

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

👍🌼

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

🎉

a = b = 9.05863

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))

Очень интересно. Спасибо

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

a=-9 b=8

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

а=-9, b=8

81-8=73 64+9=73

I loved this problem!

a=8 b=-9

:))))))))) 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

а=9 б=-8 !!!

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

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

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.