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發問:

Given that x^2 + ax + 48 = (x+y)(x+z) and x^2 - 8x - c = (x+m)(x+n), where y, z, m and n are integers between -50 and 50 inclusively. Find maximum value of ac.

最佳解答:

x^2 + ax + 48 = (x+y)(x+z) x^2 + ax + 48 = x^2 + (y+z)x + yz So a = y+z and yz = 48 The maximum value of a = y+z = 1 + 48 = 49(when yz = 1*48); x^2 - 8x - c = (x+m)(x+n) = x^2 + (m+n)x + mn So - 8 = m+n and c = - mn The maximum value of c = - (-50)(42) = 2100(when m+n = -50+42 = - 8) The maximum value of ac = 48 * 2100 = 100800 2009-12-07 17:10:58 補充： Corrections: The maximum value of ac = 49 * 2100 = 102900 Sorry! 2009-12-07 17:11:29 補充： Corrections: The maximum value of ac = 49 * 2100 = 102900 Sorry!

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