趣味數(shù)學(xué)問題懸賞1 初三、高一組參考答案

2023-09-12 13:24 作者:數(shù)學(xué)只因 0人讀過 | 我要投稿

不知道啥是趣味數(shù)學(xué)問題懸賞看這裏

第一題解答：

????1）思路：討論 x?的范圍，對每一個范圍討論其可取的最大值，再比較各范圍的最大值，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：均值過幾秒秒了，懂的自己做，不懂的看這里：

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

????接下來自己做

第二題解答：

思路：炸就完事了（均值yyds）

假設(shè)? $a%20%3D%20OA%2C%20b%20%3D%20OB%2C%20c%20%3D%20OC$

在網(wǎng)上找到計(jì)算公式，得到該錐體體積為 $%5Cfrac%7Babc%7D%7B6%7D$

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