(a+b)(a²+b²)(a³+b³)≥8a³b³
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![(a+b)(a²+b²)(a³+b³)≥8a³b³](/uploads/image/z/4001427-27-7.jpg?t=%28a%2Bb%29%28a%26%23178%3B%2Bb%26%23178%3B%29%EF%BC%88a%26%23179%3B%2Bb%26%23179%3B%EF%BC%89%E2%89%A58a%26%23179%3Bb%26%23179%3B)
(a+b)(a²+b²)(a³+b³)≥8a³b³
(a+b)(a²+b²)(a³+b³)≥8a³b³
(a+b)(a²+b²)(a³+b³)≥8a³b³
(a+b)(a²+b²)(a³+b³)=(a+b)(a²+b²)(a+b)(a²-ab+b²)
=(a+b)²(a²+b²)(a²-ab+b²)=(a²+2ab+b²)(a²+b²)(a²-ab+b²)
∵(a-b)²=a²-2ab+b²≥0
∴a²+b² ≥2ab
∴原式≥4ab×2ab×ab=8a³b³