A Nice Algebra Problem | Math Olympiad | Solve for a and b

[@oscaramorim7234]

💯

[@SALogics]

Thanks a lot ❤

[@beiranvand4066]

kzbin.info/www/bejne/gHfClKNjnt-iirMsi=kNhtLS9oObQdBEY1

[@key_board_x]

a² - b = 31 b² - a = 31 ---------------------------------------------------subtraction (a² - b) - (b² - a) = 31 - 31 a² - b - b² + a = 0 (a² - b²) + (a - b) = 0 (a + b).(a - b) + (a - b) = 0 (a - b).[(a + b) + 1] = 0 (a - b).(a + b + 1) = 0 First case: (a - b) = 0 a - b = 0 a = b Restart from: a² - b = 31 a² - b = 31 → where: a = b a² - a = 31 a² - a - 31 = 0 Δ = (- 1)² - (4 * - 31) = 1 + 124 = 125 a = (1 ± √125)/2 a = (1 ± 5√5)/2 First solution: → a = (1 + 5√5)/2 → b = (1 + 5√5)/2 Second solution: → a = (1 - 5√5)/2 → b = (1 - 5√5)/2 Second case: (a + b + 1) = 0 a + b + 1 = 0 b = - 1 - a Restart from: a² - b = 31 a² - b = 31 → where: b = - 1 - a a² - (- 1 - a) = 31 a² + 1 + a = 31 a² + a - 30 = 0 Δ = (1)² - (4 * - 30) = 1 + 120 = 121 = 11² a = (- 1 ± 11)/2 Third solution: a = (- 1 + 11)/2 → a = 5 Recall: b = - 1 - a b = - 1 - 5 → b = - 6 Fourth solution: a = (- 1 - 11)/2 → a = - 6 Recall: b = - 1 - a b = - 1 + 6 → b = 5

[@SALogics]

Very nice! I really appreciate that ❤

[@beiranvand4066]

kzbin.info/www/bejne/gHfClKNjnt-iirMsi=kNhtLS9oObQdBEY1

[@cabasantbab]

A = -6 B = 5

[@SALogics]

Yes, what about other 3 solutions? ❤

[@beiranvand4066]

kzbin.info/www/bejne/gHfClKNjnt-iirMsi=kNhtLS9oObQdBEY1

[@isaacsalomonmatusortiz615]

Buenas tardes. Error falta. a,b 1+5√5/2; 1+5√5/2 a,b 1-5√5/2; 1-5√5/2

[@isaacsalomonmatusortiz615]

Estoy lleva a confusión del problema. Isaac Matus,from Santiago de Chile,South América. Thanks so much for your teachin. My English is poor

[@SALogics]

Sí, lo olvidé. ¡Muchas gracias por señalarlo! ❤

[@mercedesclaveras]

Falta partido 2 cuando a es igual a b

[@SALogics]

Sí, lo olvidé. ¡Muchas gracias por señalarlo! ❤

[@beiranvand4066]

kzbin.info/www/bejne/gHfClKNjnt-iirMsi=kNhtLS9oObQdBEY1