標題:
搵高手解釋下以下的狀況(a.maths)
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發問:
其實我有初步概念 有少少明佢做緊咩 但係要表達出黎又好似唔太識 例如: a^k - b^k = (a-b)M = a^k+1 - b^k+1 = (a)a^k - b^k (b) = (a)a^k - ab^k +ab^k -(b)b^k 我知道係關於 (a)a^k - b^k (b) 左右方都x a/b 出黎 但我想要清楚一步 知道 點解左右邊要x 個 a/b 更新: = = 我係唔知點解釋個(a)a^k - b^k (b)------->(a)a^k - ab^k +ab^k -(b)b^k 呢過程 唔係唔識計= =
最佳解答:
a^k - b^k = (a-b)M a^k - b^k = a^k+1 - b^k+1 = (a)a^k - b^k (b) = (a)a^k - ab^k + ab^k -(b)b^k - ba^k + ba^k = (a -b)a^k + (a-b)b^k + ab^k -ba^k = (a-b) (a^k +b^k) - ab[a^(k-1) - b^(k-1)] a-b is one of the factor of the portion [a^(k-1) - b^(k-1)] Therefore a^(k+1) - b^(k+1) is divisble by (a-b) 2008-08-15 17:11:38 補充： (a)a^k - b^k (b) 加一個 Term 另到(a)a^k 做成有 a^k - b^k在內, 這個a^k - b^k term可以被 a-b 除盡
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