第5章 5.5

(1)

$x^2 - 4x + 2 = 2x - 3$

$x^2 - 6x + 5 = 0 \qquad (x-5)(x-1) = 0 \qquad x = 1, 5$

$x = 1$ のとき $y = -1$ $x = 5$ のとき $y = 7$

よって共有点の座標は$(1, -2), (5, -7)$

(2)

$-2x^2 + 6x - 5 = -2x + 3$

$2x^2 - 8x + 8 = 0 \qquad 2(x^2 - 4x + 4) = 0 \qquad 2(x-2)^2 = 0 \qquad x = 2$

$x = 2$ のとき $y = -1$

よって共有点の座標は$(2, -1)$

(3)

$3x^2 + 5x + 7 = x + 5$

$3x^2 + 4x + 2 = 0 \qquad x = \frac{-2 \pm \sqrt{4-6}}{3} = \frac{-2 \pm \sqrt{2}i}{3}$

よって共有点はなく虚数解は$\dfrac{-2 \pm \sqrt{2}i}{3}$