Question

[su_00]

Cho 4 số không âm a, b, c, d. Chứng minh rằng: 

\(\left(\frac{a+b+c+d}{4}\right)^4\ge abcd\)

Answer 1

[Phạm Thế Mạnh]

Có:\(a+b+c+d\ge4\sqrt[4]{abcd}\)(BĐT Cô-si)
\(\Rightarrow\frac{a+b+c+d}{4}\ge\frac{4\sqrt[4]{abcd}}{4}=\sqrt[4]{abcd}\)
\(\Rightarrow\left(\frac{a+b+c+d}{4}\right)^4\ge abcd\)
Dấu "=" xảy ra \(\Leftrightarrow a=b=c=d\)