Question

Calcule o x1 e x2 das equações
X²‐5x+6=0
X²‐3x+5=0
X²‐9=0

Answer 1

Resposta:

x1 = $\frac{2}{3} + \frac{\sqrt{11}}{2} i$

x2 = $\frac{2}{3} - \frac{\sqrt{11}}{2} i$

Explicação passo a passo:

x = $\frac{- (-3)+-\sqrt{(-3)² -4 . 1. 5}}{2 . 1}$

x = $\frac{3+-\sqrt{(-3)² -4. 5}}{2}$

x = $\frac{3+-\sqrt{9-20}}{2}$

x = $\frac{3+-\sqrt{-11}}{2}$   → $\sqrt{-11}$ ⇒$\sqrt[]{11.(-1)}$ ⇒ $\sqrt{11}$ . $\sqrt{-1}$ ⇒ $\sqrt{11} i$

x = $\frac{3+-\sqrt{-11}i}{2}$

x1 = $\frac{3+\sqrt{-11}i}{2}$ =  $\frac{2}{3} + \frac{\sqrt{11}}{2} i$

x2 = $\frac{3-\sqrt{-11}i}{2}$ = $\frac{2}{3} - \frac{\sqrt{11}}{2} i$