Question

As raízes da equação (x -3) ao quadrado=-2x são?

Rapido​

Answer 1

Resposta:

(x-3)²= -2x

x²-6x+9= -2x

x²-4x+9=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-4x+9=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-4~e~c=9\\\Delta=(b)^{2}-4(a)(c)=(-4)^{2}-4(1)(9)=16-(36)=-20\\\sqrt{\Delta}=\sqrt{-20}=\sqrt{(-1)(20)} =\sqrt{-1}.\sqrt{2^{2}.5}=i2\sqrt{5}\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-4)-i2\sqrt{5}}{2}=2-i\sqrt{5}\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-4)+i2\sqrt{5}}{2}=2+i\sqrt{5}\\S=\{2-i\sqrt{5},2+i\sqrt{5}\}$