Asignatura: Matemáticas
Autor: Julimayo
hace 3 años

resuelve 3x² -8x-3=0

Respuestas

Respuesta dada por: roycroos

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

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

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

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

Reemplazamos los coeficientes en la fórmula general:

$\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{-(-8) \pm \sqrt{(-8)^2 - [4(3)(-3)]}}{2(3)}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{8 \pm \sqrt{64 - (-36)}}{6}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{8 \pm \sqrt{100}}{6}}\\\\\\\center \mathrm{x_{1,2}} \mathrm{= \dfrac{8 \pm 10}{6}}$

$\center \Rightarrow\:\mathrm{x_{1}} \mathrm{= \dfrac{8 + 10}{6}}\\\\\\\center \mathrm{x_{1}} \mathrm{= \dfrac{18}{6}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{1}} \mathrm{= 3}}}}\\\\\\.\\.$ $\center \Rightarrow\:\mathrm{x_{2}} \mathrm{= \dfrac{8 - 10}{6}}\\\\\\\center \mathrm{x_{2}} \mathrm{= \dfrac{-2}{6}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{2}} \mathrm{= -\dfrac{1}{3}}}}}$