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趣味數學問題懸賞1 初三、高一組 參考答案

2023-09-12 13:24 作者:数学只因  | 我要投稿

不知道啥是趣味數學問題懸賞看這裏

第一题解答:

    1)思路:讨论 x 的范围,对每一个范围讨论其可取的最大值,再比较各范围的最大值,求出 m 

    2) 思路一:柯西秒了,懂的自己做,不懂的看思路二

        思路二:均值过几秒秒了,懂的自己做,不懂的看这里:

    %5Cbegin%7Balign%7D%0A%26(2a%2B3b%2B4c)(%5Cfrac%7B1%7D%7B2a%7D%2B%5Cfrac%7B1%7D%7B3b%7D%2B%5Cfrac%7B1%7D%7B4c%7D)%5C%5C%0A%3D%261%2B%5Cfrac%7B2a%7D%7B3b%7D%2B%5Cfrac%7B2a%7D%7B4c%7D%2B%5Cfrac%7B3b%7D%7B2a%7D%2B1%2B%5Cfrac%7B3b%7D%7B4c%7D%2B%5Cfrac%7B4c%7D%7B2a%7D%2B%5Cfrac%7B4c%7D%7B3b%7D%2B1%5C%5C%0A%5Cgeq%263%20%2B%202%5Csqrt%7B%5Csqrt%7B%5Cfrac%7B3b%7D%7B2a%7D%5Ccdot%5Cfrac%7B2a%7D%7B3b%7D%7D%7D%2B2%5Csqrt%7B%5Csqrt%7B%5Cfrac%7B3b%7D%7B4c%7D%5Ccdot%5Cfrac%7B4c%7D%7B3b%7D%7D%7D%2B2%5Csqrt%7B%5Csqrt%7B%5Cfrac%7B4c%7D%7B2a%7D%5Ccdot%5Cfrac%7B2a%7D%7B4c%7D%7D%7D%5C%5C%0A%3D%26%5Cspace%209%0A%5Cend%7Balign%7D

    接下來自己做

第二题解答:

思路:炸就完事了(均值yyds)

假设 a%20%3D%20OA%2C%20b%20%3D%20OB%2C%20c%20%3D%20OC

在网上找到计算公式,得到该锥体体积为%5Cfrac%7Babc%7D%7B6%7D

%5Cbegin%7Balign%7D%0A6%20%26%3D%20%20a%2Bb%2Bc%2B%5Csqrt%7Ba%5E2%2Bb%5E2%7D%2B%5Csqrt%7Bb%5E2%2Bc%5E2%7D%2B%5Csqrt%7Bc%5E2%2Ba%5E2%7D%5C%5C%0A%26%5Cgeq3%5Csqrt%5B3%5D%7Babc%7D%2B%5Csqrt%7B2ab%7D%2B%5Csqrt%7B2bc%7D%2B%5Csqrt%7B2ca%7D%5C%5C%0A%26%5Cgeq%203%5Csqrt%5B3%5D%7Babc%7D%2B3%5Csqrt%5B3%5D%7B%5Csqrt%7B2ab%7D%5Ccdot%5Csqrt%7B2bc%7D%5Ccdot%5Csqrt%7B2ca%7D%7D%5C%5C%0A%26%3D3%5Csqrt%5B3%5D%7Babc%7D%2B3%5Csqrt%7B2%7D%5Csqrt%5B3%5D%7Babc%7D%5C%5C%26%3D%20(3%2B3%5Csqrt%7B2%7D)%5Csqrt%5B3%5D%7Babc%7D%5C%5C%0A%5Ctherefore%20%5Cfrac%7Babc%7D%7B6%7D%20%26%5Cleq%20%5Cfrac%7B(%5Cfrac%7B6%7D%7B3%2B3%5Csqrt%7B2%7D%7D)%5E3%7D%7B6%7D%20%3D%20%5Cfrac%7B(2%5Csqrt%7B2%7D-2)%5E3%7D%7B6%7D%3D%5Cfrac%7B40%5Csqrt%7B2%7D-56%7D%7B6%7D%3D%5Cfrac%7B20%5Csqrt%7B2%7D-28%7D%7B3%7D%0A%5Cend%7Balign%7D




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