论文部分内容阅读
1把演算技巧上升为数学法则首先观察下面一些代数不等式:1)(a+b+c)/3≤((a~2+b~+c~2)/3)~(1/2)2)a~3+b~3+c~3≥3abc3)ab~(1/2)+bc~(1/3)+ac~(1/2)≤a+b+c4)1/(a+b+c)≤1/9(1/a+1/b+1/c)我们还有一个经典的均值不等式:(?)≤(a_1+a_2+…a_x)/n,其含义是n个正实数的几何平均值不大于它们的算术平均值.根据解不等式或证明不等式的经验,上面一系列不等式与经典的均值不等式具有相当密切的关联性,但是如何利用经典均值不等式来证明它们还需要
1 Raise the Arithmetic Skills to Mathematical Rules First observe the following algebraic inequalities: 1) (a + b + c) / 3 ≤ ((a ~ 2 + b ~ + c ~ 2) / 3) ) a~3 + b~3 + c~3≥3 abc3) ab~ (1/2) + bc~ (1/3) + ac~ (1/2) ≦ a + b + c4) 1 / (a + we have a classical mean inequality: (?) ≤ (a_1 + a_2 + ... a_x) / n, which means n positive The geometric mean of real numbers is not greater than their arithmetic mean.According to the experience of solving inequalities or proving inequalities, the above series of inequalities are quite closely related to classical mean inequalities, but how to prove them with classical mean inequality