第5章 5.5

(1)

x24x+2=2x3x^2 - 4x + 2 = 2x - 3

x26x+5=0(x5)(x1)=0x=1,5x^2 - 6x + 5 = 0 \qquad (x-5)(x-1) = 0 \qquad x = 1, 5

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

よって共有点の座標は(1,2),(5,7)(1, -2), (5, -7)

(2)

2x2+6x5=2x+3-2x^2 + 6x - 5 = -2x + 3

2x28x+8=02(x24x+4)=02(x2)2=0x=22x^2 - 8x + 8 = 0 \qquad 2(x^2 - 4x + 4) = 0 \qquad 2(x-2)^2 = 0 \qquad x = 2

x=2x = 2 のとき y=1y = -1

よって共有点の座標は(2,1)(2, -1)

(3)

3x2+5x+7=x+53x^2 + 5x + 7 = x + 5

3x2+4x+2=0x=2±463=2±2i33x^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2±2i3\dfrac{-2 \pm \sqrt{2}i}{3}

解説: r31bn1z