设a,b,c,d是正实数,证明:a+b+c+d/abcd≤1/a^3+1/b^3+1/c^3+1/d^3
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![设a,b,c,d是正实数,证明:a+b+c+d/abcd≤1/a^3+1/b^3+1/c^3+1/d^3](/uploads/image/z/5468335-7-5.jpg?t=%E8%AE%BEa%2Cb%2Cc%2Cd%E6%98%AF%E6%AD%A3%E5%AE%9E%E6%95%B0%2C%E8%AF%81%E6%98%8E%3Aa%2Bb%2Bc%2Bd%2Fabcd%E2%89%A41%2Fa%5E3%2B1%2Fb%5E3%2B1%2Fc%5E3%2B1%2Fd%5E3)
设a,b,c,d是正实数,证明:a+b+c+d/abcd≤1/a^3+1/b^3+1/c^3+1/d^3
设a,b,c,d是正实数,证明:a+b+c+d/abcd≤1/a^3+1/b^3+1/c^3+1/d^3
设a,b,c,d是正实数,证明:a+b+c+d/abcd≤1/a^3+1/b^3+1/c^3+1/d^3
(1/(3a^3)+1/(3b^3)+1/(3c^3))/3>=三次根号(1/(3a^3)*1/(3b^3)*1/(3c^3))=1/(3abc)
1/(3a^3)+1/(3b^3)+1/(3c^3)>=1/(abc)=d/abcd
同理
1/(3a^3)+1/(3c^3)+1/(3d^3)>=1/(acd)=b/abcd
1/(3a^3)+1/(3b^3)+1/(3c^3)>=1/(abd)=c/abcd
1/(3b^3)+1/(3c^3)+1/(3d^3)>=1/(bcd)=a/abcd
四式相加,得证