Question

Como fazer :

x²+x+1=0

Answer 1

$x^{2} + x + 1 = 0$

$x = \dfrac{-b \pm \sqrt{b^2 -4*a*c}}{2*a}$

a=1, b=1, c=1

Δ=b²−4ac
Δ=(1)²−4*(1)*(1)
Δ=1−4
Δ= −3

$x = \dfrac{-b \pm \sqrt{\triangle}}{2*a} \\ \\ \\ x = \dfrac{-1 \pm \sqrt{-3}}{2*1} \\ \\ \\ x = \dfrac{-1 \pm \sqrt{3}*i}{2} \\ \\ \\ x' = \dfrac{-1 + \sqrt{3} *i}{2} \\ \\ \\ x' = \dfrac{-1 - \sqrt{3}*i}{2}$


S = {$\dfrac{-1 + \sqrt{3}*i}{2}, \ \ \dfrac{-1 - \sqrt{3}*i}{2}$}

Answer 2

x² +x +1 =0

Δ=b²-4ac
Δ=1²-4(1)
Δ=1-4
Δ=-3

$x= \frac{-1\pm \sqrt{-3} }{2} = \frac{-1\pm \sqrt{i^23} }{2} = \frac{-1\pm i \sqrt{3} }{2} \\ \\ x'= \frac{-1+i \sqrt{3} }{2} \\ \\ x"= \frac{-1-i \sqrt{3} }{2}$