方程式論！！求解

AP = 等差數列， GP =等比數列 f(x) = x^3 + 3x^2 + mx – ng(x) = x^3 + (2-m)x^2 –(n+3)x – 8 f(x) = 0 三根 a –d, a, a+dg(x) = 0三根 b/r, b, br f(x) = 0 三根和 = (a –d) + a + (a+d) = 3a = -3, a = -1g(x) = 0 三根積 = (b/r)(r)(br) = b^3 = -(-8), b = 2 f(x) = 0 三根 -1 –d, -1, -1+dg(x) = 0三根 2/r, 2, 2r f(x) = 0 三根之兩兩積和 = (-1-d)(-1) + (-1)(-1+d) + (-1+d)(-1-d) = mf(x) = 0 三根積 = (-1-d)(-1)(-1+d) = -(-n) m = 1+d + 1 –d + 1 – d^2 = -d^2 + 3 ---(1)n = d^2 – 1 --- (2) (1) + (2)：m + n = 2 --- (3) g(x) = 0 三根和 = (2/r) + (2) + (2r) = -(2-m)g(x) = 0 三根之兩兩積和 = (2/r)(2) + (2)(2r) + (2r)(2/r) = -(n+3) m + 2 = (2/r)(r^2 + r + 1) --- (4)-(n+3) = (4/r)(r^2 + r + 1) --- (5) (4)÷(5)：-(m+2)/(n+3) = 1/2 -2m + 4 = n + 32m + n = 1 ----(6) (6) – (3)：m = -1 代入(3), n = 3 Ans：m = -1, n = 3

2014-08-16 19:16:05 補充：
確實...

受教了

你两位都好鬼厲害。

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C 網友，其實可以簡單一點。

由於 -1 是 f(x) = 0 的根，那麼 f(-1) = 0 得 m + n = 2
由於 2 是 g(x) = 0 的根，那麼 g(2) = 0 得 2m + n = 1

m = -1
n = 3

2014-08-16 19:32:23 補充：
客氣客氣～

多多指教～

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