Question

Determinati solutiile COMPLEXE ale ecuatiei x^2-6x+10=0

Answer 1

$D= b^{2}-4ac=36-40=-10 \\ x_{1}= \frac{-b+ \sqrt[]{D} }{2a}= \frac{6+i \sqrt[]{10} }{2}=3+i \frac{\sqrt[]{10}}{2} \\ x_{2}= \frac{-b- \sqrt[]{D} }{2a}=3-i\frac{\sqrt[]{10}}{2}$

Answer 2

      
$x^{2} -6x+10=0 \\ \\ x_{12} = \frac{-b \pm \sqrt{ b^{2} -4ac}}{2a} \\ \\ x_{12} = \frac{-(-6) \pm \sqrt{ (-6)^{2} -4*1*10}}{2*1} \\ \\ x_{12} = \frac{6 \pm \sqrt{ 36 -40}}{2}=\frac{6 \pm \sqrt{-4}}{2}=\frac{6 \pm 2i}{2} = 3 \pm i \\ \\ x_1 = \boxed{3+i} \\ x_2 = \boxed{3-i}$