Answer:
[tex] y^2 -4y +6=0[/tex]
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where [tex] a = 1, b= -4 ,c =6[/tex]
And replacing we got:
[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]
And solving we got:
[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]
Where [tex] i =\sqrt{-1}[/tex]
And the possible solutions are:
[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]
Step-by-step explanation:
For this case we use the equation given by the image and we have:
[tex] -y^2 +4y -6=0[/tex]
We can rewrite the last expression like this if we multiply both sides of the equation by -1.
[tex] y^2 -4y +6=0[/tex]
Now we can use the quadratic formula given by:
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where [tex] a = 1, b= -4 ,c =6[/tex]
And replacing we got:
[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]
And solving we got:
[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]
Where [tex] i =\sqrt{-1}[/tex]
And the possible solutions are:
[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]
