Question

Resolva em números complexos a seguinte equação;
x²-2x+7=0

Answer 1

Olá William!

Resposta:

$\boxed{\mathtt{S = \left \{1 + i\sqrt{6}; 1 - i\sqrt{6} \right \}}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{x^2 - 2x + 7 = 0} \\\\ \mathsf{\Delta = (- 2)^2 - 4 \cdot 1 \cdot 7} \\\\ \mathsf{\Delta = 4 - 28} \\\\ \mathsf{\Delta = - 24} \\\\ \mathsf{\Delta = 24 \cdot (- 1)} \\\\ \mathsf{\Delta = 24i^2}$

Com efeito,

$\\ \displaystyle \mathsf{x = \frac{- (- 2) \pm \sqrt{24i^2}}{2}} \\\\\\ \mathsf{x = \frac{2 \pm \sqrt{4i^2 \cdot 6}}{2}} \\\\\\ \mathsf{x = \frac{2 \pm 2i\sqrt{6}}{2}} \\\\ \mathsf{x = 1 \pm i\sqrt{6}}$

Isto é, $\displaystyle \\ \boxed{\boxed{\mathsf{x_1 = 1 + i\sqrt{6}}}}$ e $\displaystyle \\ \boxed{\boxed{\mathsf{x_2 = 1 - i\sqrt{6}}}}$