Question

a. (x+2)(x-3)=6
b. (x+1)(x-5)=16
resolver la ecuación usando la fórmula general para resolver ecuaciones cuadráticas ​

Answer 1

Respuesta:

Explicación paso a paso:

a)  (x+2)(x-3)=6

$x^{2} -x-6=6$

$x^{2} -x-12=0$

$a=1, b=-1, c= -12$

calculamos la discriminante

$d = {b^{2} - 4ac}$

$d = (-1)^{2} - (4)(1)(-12)} = 1 + 48 = 49$

$x1= \frac{-(-1) + \sqrt{49} }{2(1)} =\frac{1+7}{2} = 4$

$x2= \frac{-(-1) - \sqrt{49} }{2(1)} = \frac{1-7}{2} = -3$

b) (x+1)(x-5)=16

$x^{2} -4x-5=16$

$x^{2} -4x-21= 0$

$a=1, b=-4, c= -21$

$d = {(-4)^{2} - 4(1)(-21)} = 16 + 84 = 100$

$\\x1= \frac{-(-4) + \sqrt{100} }{2(1)} =\frac{4+10}{2} = 7$

$\\x2= \frac{-(-4) - \sqrt{100} }{2(1)} =\frac{4-10}{2} = -3$