Question

deduza a fórmula de bháskara ,isolando o x na equação : ax2+bx+c=0

Answer 1

Olá!
 
 
    $ax^2+bx+c=0\overset{a\neq 0}{\Longrightarrow} x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\Rightarrow \left(x+\dfrac{b}{2a}\right)^2-\dfrac{b^2}{4a^2}+\dfrac{c}{a}=0\\ \text{Ent\~ao}\\ \left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2}{4a^2}-\dfrac{c}{a}\Rightarrow \left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2-4ac}{4a^2}\Rightarrow\\ \\ \Rightarrow \left(x+\dfrac{b}{2a}\right)^2=\dfrac{\Delta}{4a^2}\Rightarrow x+\dfrac{b}{2a} = \pm\sqrt{\dfrac{\Delta}{4a^2}}\Rightarrow$

$\Rightarrow x+\dfrac{b}{2a} = \pm\dfrac{\sqrt{\Delta}}{\sqrt{4a^2}}\Rightarrow x+\dfrac{b}{2a}=\pm\dfrac{\sqrt{\Delta}}{2a}\Rightarrow \\ \\ \Rightarrow x=-\dfrac{b}{2a}\pm\dfrac{\sqrt{\Delta}}{2a}\Rightarrow x = \dfrac{-b\pm\;\sqrt{\Delta}}{2a}.$




Bons estudos!