quadratic equation

2009-09-25 5:01 am

1. Solve 25x^2-25x-6=0

2. The cost of a diamond is $120 000. Mary sold it to Helen at a profit of r%. After one year, Helen sold the diamond back to Mary at a profit of r%. As a result, Mary lost $28 800. Find the value of r.

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回答 (1)

用戶9112

2009-09-25 5:12 am

✔ 最佳答案

1. 25x^2 - 25x - 6 = 0
25x^2 - 30x + 5x - 6 = 0
5x(5x - 6) + (5x - 6) = 0
(5x + 1)(5x - 6) = 0
x = -0.2 or x = 1.2
2. Selling price from Mary to Helen = $120,000 * (1 + r/100)
Selling price from Helen back to Mary = $120,000 * (1 + r/100)^2
Loss of Mary = $120,000 * (1 + r/100)^2 - $120,000 * (1 + r/100) = 28,800
120000(1 + r/100)(1 + r/100 - 1) = 28800
(1 + r/100)(r/100) = 0.24
r/100 + r^2/10000 = 0.24
100r + r^2 = 2400
r^2 + 100r - 2400 = 0
(r +120)(r - 20) = 0
r = 20 or r = -120(rejected)

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