第4章 4.7

(1)

$x^2 + x + 3 = 0$

$x = \frac{-1 \pm \sqrt{1-12}}{2} = \frac{-1 \pm \sqrt{11}i}{2}$

(2)

$x^2 - 2x + 2 = 0$

$x = 1 \pm \sqrt{1-2} = 1 \pm i$

(3)

$x^2 - 4x + 6 = 0$

$x = 2 \pm \sqrt{4-6} = 2 \pm \sqrt{2}i$

(4)

$x - 2 = 2x^2 + 2 \qquad 2x^2 - x + 4 = 0$

$x = \frac{1 \pm \sqrt{1-32}}{4} = \frac{1 \pm \sqrt{31}i}{4}$

(5)

$\frac{x^2+1}{2} = x - 1 \qquad x^2 + 1 = 2x - 2 \qquad x^2 - 2x + 3 = 0$

$x = 1 \pm \sqrt{1-3} = 1 \pm \sqrt{2}i$

(6)

$\frac{x^2}{3} - \frac{x}{5} + \frac{13}{30} = 0 \qquad 10x^2 - 6x + 13 = 0$

$x = \frac{3 \pm \sqrt{9-130}}{10} = \frac{3 \pm \sqrt{121}i}{10} = \frac{3 \pm 11i}{10}$