美夢成真教甄討論區

請問 一題代數

設 f(x) = 0 之整數根為 k，且 k ＞ a ≧ b ≧ c ≧ d

(k - a)(k - b)(k - c)(k - d) = 28 = 1 * 1 * 1 * 28 = 1 * 1 * 4 * 7 = 1 * 2 * 2 * 7

(1) k - a = k - b = k - c = 1，k 最大是 21，但 k - d = 28，不合

(2) k - a = k - b = 1，k - c = 4，k - d = 7
a 和 b 取 20，c = 17，d = 14
a + b + c + d = 71

(3) k - a = 1，k - b = 2，k - c = 2，k - d = 7
a 取 20，b = 19，c = 19，d = 14
a + b + c + d = 72

所求為 72