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標題:

f4 math question

發問:

Show that 32 can be divided into four part T(1), T(2), T(3), T(4) which are in Arithmetic Series and such that T(1) X T(4) : T(2) X T(3) = 7:15

最佳解答:

Let T(1) = a, T(2) = a + d, T(3) = a + 3d and T(4) = a + 3d where a and d are some constants. Then from the given: a + (a + d) + (a + 2d) + (a + 3d) = 32 4a + 6d = 32 2a + 3d = 16 ... (1) Also: 15a(a + 3d) = 7(a + d)(a + 2d) 15a2 + 45ad = 7a2 + 14d2 + 21ad 8a2 + 24ad - 14d2 = 0 4a2 + 12ad - 7d2 = 0 (2a - d)(2a + 7d) = 0 2a = d or 2a = -7d 16 - 3d = d or 16 - 3d = -7d d = 4 or d = -4 a = 2 or a = 14 So the four parts should be 2, 6, 10 and 14 2009-04-23 11:08:54 補充： For line 1, T(3) should be a + 2d

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