Question

al efectuar (ax + b ) (x² - x + 1)

Answer 1

RESOLUCIÓN:

$(ax + b)( {x}^{2} - x + 1) \\ a {x}^{3} - a{x}^{2} + ax + b{x}^{2} - bx + b \\ a {x}^{3} - (a - b) {x}^{2} + (a - b)x + b$

Igualamos:

$a {x}^{3} - (a - b) {x}^{2} + (a - b)x + b = 7 {x}^{3} - m {x}^{2} + nx + 4$

Obtenemos:

$a {x}^{3} = 7 {x}^{3} \\ a = 7$

$b = 4$

$- (a - b) {x}^{2} = - m {x}^{2} \\ (a - b) = m \\ 7 - 4 = m \\ 3 = m$

$(a - b)x = nx \\ (a - b) = n \\ 7 - 4 = n \\ 3 = n$

RESPUESTA:

$a + b + m + n = 7 + 4 + 3 + 3 = 17$