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Cho các số thực ko âm $a,b,c$ thoã mãn $a+b+c=1$. Chứng minh :$$\sum \frac 1{\sqrt{(a^2+ab+b^2)(b^2+bc+c^2)}} \ge 4+ \frac 8{\sqrt3}$$
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Cho các số thực không âm a,b,c" role="presentation" style="display: inline; line-height: normal; font-size: 14px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(40, 40, 40); font-family: helvetica, arial, sans-serif; position: relative; background-color: rgb(255, 255, 255);">a,b,ca,b,c sao cho a+b+c=1" role="presentation" style="display: inline; line-height: normal; font-size: 14px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(40, 40, 40); font-family: helvetica, arial, sans-serif; position: relative; background-color: rgb(255, 255, 255);">a+b+c=1a+b+c=1 . Chứng minh rằng :1(a2+ab+b2)(b2+bc+c2)+1(b2+bc+c2)(c2+ca+a2)+1(c2+ca+a2)(a2+ab+b2)≥4+83" role="presentation" style="display: inline; line-height: normal; font-size: 14px; text-align: left; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; width: auto; position: relative;">1(a2+ab+b2)(b2+bc+c2)−−−−−−−−−−−−−−−−−−−−−−√+1(b2+bc+c2)(c2+ca+a2)−−−−−−−−−−−−−−−−−−−−−−√+1(c2+ca+a2)(a2+ab+b2)−−−−−−−−−−−−−−−−−−−−−−√≥4+83√1(a2+ab+b2)(b2+bc+c2)+1(b2+bc+c2)(c2+ca+a2)+1(c2+ca+a2)(a2+ab+b2)≥4+83