ecuación de la formula general que es 9x ²– 16 = 0

Respuestas

Respuesta dada por: roycroos

╔═════════════════════════════════════════════╗ $\center \mathrm{Una ecuaci\'on cuadr\'atica de la forma:}$

$\mathrm{ax^2 + bx + c=0\:\:donde\:\: a \neq 0}$

$\center \mathrm{Poseer\'a 2 soluciones x_1} \:\mathrm{y\:x_2,\:las\:cuales\:determinaremos\:por:}$

$\boldsymbol{{\mathrm{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}} \Rightarrow \boxed{\mathrm{F\'ormula\:general}}$

╚═════════════════════════════════════════════╝

Entonces a = 9, b = 0, c = -16

Reemplazamos los coeficientes en la fórmula general:

$\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-(0) \pm \sqrt{(0)^2 - [4(9)(-16)]}}{2(9)}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{\pm \sqrt{0 - (-576)}}{18}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{\pm \sqrt{576}}{18}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{\pm 24}{18}}$

$\center \Rightarrow\:\mathrm{x_{1}} \mathrm{= \dfrac{+ 24}{18}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{1}} \mathrm{= 4/3}}}}$ $\center \Rightarrow\:\mathrm{x_{2}} \mathrm{= \dfrac{- 24}{18}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{2}} \mathrm{= -4/3}}}}\\\\\\ .$