题目求最大的正数λ,使对任意实数a,b都有(a~2+ab+b~2)~3≥λa~2b~2(a+b)~2.这是前些年在《中等数学》上出现过的一道题,原来的解法需要用到一些技巧,这里用三角代换给出一个几乎不需要任何技巧的证明.解令a=b,得λ≤(27)/4,若(27)/4就是所要求的数,则 The problem is to find the largest positive number, λ, so that for any real number a, b has (a~2+ab+b~2)~3≥λa~2b~2(a+b)~2. A problem that appeared in “Middle Mathematics” requires the use of some techniques in the original solution. Here, a trigonometric substitution is used to give a proof that hardly requires any skill. The order a=b gives λ ≤ (27) / 4 If (27)/4 is the required number, then