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=2:1则a的值是

急急急啊，一会就要去考试了

求各位大侠帮忙~~~~(>_<)~~~~

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

追问

4d/3 - 4 = a/d, a = 4d(d/3 - 1) (2)
d = 3(1 + √3).2
a = 6

这里没看懂，可以给讲一下吗

追答

设D(d, a/d), D在AB上, 满足y = 4x/3 - 4: 4a/3 - 4 = a/d, a/d + 4 = 4a/3
代入(1).

其余应当容易。

Answer 2

解：连OD,则S△BCD=S△OCD=½ a
又∵S△AOB:S△BCD=2:1
∴S△AOB=a
S△AOB = ½×3×4 = 6
∴a=6