Question

resuelve x2 - 9x + 20 = 0 usando la ecuacion cuadratica x = (-b+ √b2 - 4ac) /2a ayudaa​

Answer 1

Recordemos que una ecuación cuadrática tiene la siguiente forma:

                                           $\boxed{\boldsymbol{ax^2+bx+c=0}}$

       

Por la fórmula general tenemos que:

                                    $\boldsymbol{\boxed{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}$

   

En el problema tenemos que: a = 1, b = -9, c = 20  

   

Entonces reemplazamos

                                    $\center x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\\center x_{1,2}=\dfrac{-(-9)\pm \sqrt{(-9)^2-[4(1)(20)]}}{2(1)}\\\\\\\center x_{1,2}=\dfrac{9\pm \sqrt{81-(80)}}{2}\\\\\\\center x_{1,2}=\dfrac{9\pm \sqrt{1}}{2}\\\\\\\center x_{1,2}=\dfrac{9\pm1}{2}$

                                                    $\center \Rightarrow\:x_{1}=\dfrac{9+1}{2}\\\\\\\center x_{1}=\dfrac{10}{2}\\\\\\\center \boxed{\boxed{\boldsymbol{x_{1}=5}}}\\\\\\\\\center \Rightarrow\:x_{2}=\dfrac{9-1}{2}\\\\\\\center x_{2}=\dfrac{8}{2}\\\\\\\center \boxed{\boxed{\boldsymbol{x_{2}=4}}}$

                                                                                                          〆ʀᴏɢʜᴇʀ ✌

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