Asignatura: Física
Autor: jesusrey24
hace 4 años

x²-2x+1=0 ecuacion cuadratica con la formula general

Respuestas

Respuesta dada por: roycroos

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

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

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

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

En el problema

$\mathsf{\underbrace{\boldsymbol{1}}_{a}x^2\:\underbrace{\boldsymbol{-\:\:2}}_{b}x\:+\:\underbrace{\boldsymbol{1}}_{c}=0}$

Entonces a = 1, b = -2, c = 1

Reemplazamos los coeficientes en la fórmula general:

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

$\center \Rightarrow\:\mathrm{x_{1}} \mathrm{= \dfrac{2 + 0}{2}}\\\\\\\center \mathrm{x_{1}} \mathrm{= \dfrac{2}{2}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{1}} \mathrm{= 1}}}}$ $\center \Rightarrow\:\mathrm{x_{2}} \mathrm{= \dfrac{2 - 0}{2}}\\\\\\\center \mathrm{x_{2}} \mathrm{= \dfrac{2}{2}}\\\\\\\center \boxed{\boxed{\boldsymbol{\mathrm{x_{2}} \mathrm{= 1}}}}$