Question

Resolva as equações a seguir: x2-2x+2=0

Answer 1

Resposta:

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-2x+2=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-2~e~c=2\\\\\Delta=(b)^{2}-4(a)(c)=(-2)^{2}-4(1)(2)=4-(8)=-4\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-2)-\sqrt{-4}}{2(1)}=\frac{2-i\sqrt{4}}{2}=\frac{2-2i}{2}=1-i\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-2)+\sqrt{-4}}{2(1)}=\frac{2+i\sqrt{4}}{2}=\frac{2+2i}{2}=1+i\\\\\\\\\\S=\{1-i,~1+i\}$

Onde: i=√-1