证明:a^4+b^4+c^4+d^4≥4abcd
问题描述:
证明:a^4+b^4+c^4+d^4≥4abcd
答
∵ a^2 + b^2 ≥ 2ab
∴[a^4+b^4]+[c^4+d^4]
≥ [2a^2b^2] + [2c^2d^2]
= 2 [a^2b^2+ c^2d^2]
≥ 2 [2abcd]= 4abcd