Cho các số thực ko âm $a,b,c$ thoã mãn $a+b+c=1$. Chứng minh :
$$\sum \frac 1{\sqrt{(a^2+ab+b^2)(b^2+bc+c^2)}} \ge 4+ \frac 8{\sqrt3}$$
Bài này không đẹp bằng bài toán xuất phát điểm của nó, ta dùng bài toán ban đầu của anh Cẩn làm bổ đề cho bài này. Xem bài 16 tại đây:

http://k2pi.net.vn/showthread.php?t=25245

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