※ 引述《hotplushot (熱加熱)》之銘言：
: a>0, b>0, c>0, a+b+c=1,
: 求(a+1/a)^3+(b+1/b)^3+(c+1/c)^3最小值
(a+1/a)^3 = a^3 + 3a + 3/a + 1/a^3
算幾不等式:
(1) a^3 + 1/27 + 1/27 ≧3*(1/9)*a = a/3
(2) 3/a + 27a ≧18
(3) 1/a^3 + 81a + 81a +81a ≧4*27 = 108
=> (a+1/a)^3 + (2/27) + 27a + 243a ≧(10/3)a + 126
=> (a+1/a)^3 ≧(126 - (2/27)) - (270 - (10/3))a
=> (a+1/a)^3+(b+1/b)^3+(c+1/c)^3 ≧(378 - (2/9)) - (270 - (10/3)) = 1000/9
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◆ From: 18.108.6.4