Question

如图10 直线y=4/3x-4交坐标轴于AB两点,与双曲线y=a/x交与点D,DC⊥x轴于点C,S△aob:S△bcd=

Answer 1

x = 0, y = -4, B(0, -4)

y = 0, x = 3, A(3, 0)

AOB的面积 = (1/2)*3*4 = 6

BCD的面积 = 6/2 = 3

D(d, a/d)

BCD的面积 = ABC的面积 + ACD的面积

= (1/2)(d - 3)*4 + (1/2)(d - 3)*a/d

= (1/2)(d- 3)(4 + a/d) = 3 (1)

D在直线上: 4d/3 =4 + a/d (2)

(2)代入(1): 2d² - 6d - 9 = 0

d = 3(1 + √3)/2 (舍去负根)

代入(2): a = 6