Question

resolvendo a seguinte equaçao completa do 2 grau: x2 - 6x + 40 = 0, quais sao as raizes encontradas?

Answer 1

Resposta:

$x_1=3+\sqrt{31}\\\:x_2=3-\sqrt{31}$

Explicação passo-a-passo:

$x^2-6x+40=0\\x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:40}}{2\cdot \:1}\\x_{1,\:2}=\frac{-\left(-6\right)\pm \:2\sqrt{31}i}{2\cdot \:1}\\x_1=\frac{-\left(-6\right)+2\sqrt{31}i}{2\cdot \:1},\:x_2=\frac{-\left(-6\right)-2\sqrt{31}i}{2\cdot \:1}$

$\frac{-\left(-6\right)+2\sqrt{31}i}{2\cdot \:1}\\=\frac{6+2\sqrt{31}i}{2\cdot \:1}\\=\frac{6+2\sqrt{31}i}{2}\\\\=\frac{2\left(3+\sqrt{31}i\right)}{2}\\=3+\sqrt{31}i$

$\frac{-\left(-6\right)-2\sqrt{31}i}{2\cdot \:1}\\=\frac{6-2\sqrt{31}i}{2\cdot \:1}\\=\frac{2\left(3-\sqrt{31}i\right)}{2}\\=3-\sqrt{31}i$

$x_1=3+\sqrt{31}i,\:x_2=3-\sqrt{31}i$