中五數學(續二次方程)

2/(1 - i) = 2(1 + i)/[(1 - i)(1 + i)] = (2 + 2i)/(1 + 1) = 2(1 + i)/2 = 1 + i.

2012-06-21 06:53:08 補充：
Let x = a + bi. So (a + bi) + (3 - 5i) = 2/(1 - i) = 1 + i
(a + 3) + (b - 5)i = 1 + i. So a = - 2 and b = 6. That is x = - 2 + 6i.

2012-06-21 06:58:36 補充：
(17) Let time required for P to fill the tank alone = x min. So time required by Q alone = (x - 6) min.
In 1 min. P alone can fill 1/x of the tank. In 1 min. Q alone can fill 1/(x - 6) of the tank. In 1 min., P and Q together can fill 1/(40/3) = 3/40 of the tank.
So 1/x + 1/(x - 6) = 3/40.

2012-06-21 07:04:57 補充：
40(x - 6) + 40x = 3x(x - 6). 80x - 240 = 3x^2 - 18x. 3x^2 - 98x + 240 = 0. (x - 30)(3x - 8) = 0
so x = 30 or 8/3 (reject because P alone cannot be faster than P and Q together.) That is P alone can fill in 30 min. and Q alone can fill in 24 min.

2012-06-21 07:08:36 補充：
Note : If P = 8/3, Q will be negative which is not possible. So x = 8/3 is rejected.