關於數學的問題? (20分)

[匿名]

2010-12-13 7:02 am

1.the speed of the water current is xkm/h. the speed of a boat in still water is x^2 km/h.
After 1.5 hours upstream and 1 hour downstream, the boat has moved 26 km.
write an equation in x.
find x.
請用中文解釋呢條!

2.if the equation x^2+KX+x=0 has equal roots.find the value of k

3. solve the quadratic inequalities x^2-7x-8≧0.

回答 (1)

用戶25568

2010-12-13 8:55 am

✔ 最佳答案

1. 設向上游為正距離，並且26公里指向上游
水流向下游，速度則為 -x，船速度則為+-x^2視乎上下游
船向上游時，速度為(x^2 - x)
船向下游時，速度為(-x^2 - x)

1.5 * (x2 - x) - 1 (x2 + x) = 26

1.5 x2 - 1.5x - x2 - x = 26
0.5x2 - 2.5x - 26 = 0
之後請自行使用 quadratic equation

2. 公式有唯一解，則判別式 b^2 - 4ac = 0

b = k, a = c = 1
k^2 - 4 = 0

如果 x^2 - 4 = 0
quadratic 解出 x = +- 2
因此 k = +-2

3. 判斷算式 b^2 - 4ac = 49 - 32 = 17
公式有兩個實數解
x^2 - 7x - 8 = (x + 1)(x - 8)
根為 -1 和 8
項數A > 0
因此 x < -1 或 x > 8

4. 題目是 4x^2-(k+2)x+k-1=0吧？
有兩等根，代表判別式b^2 - 4ac = 0
(k+2)^2 - 4 * 4 * (k-1) = 0
再構作k的二元一次方程，再用quadratic解出k

別這麼依賴了，暫時幫到這裡

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