Cho các số thực $a, b, c, d$ thỏa $a+ b+ c= 3$. CM: $\frac{a}{1+ 3b^{4}}+ \frac{b}{1+ 3c^{4}}+ \frac{c}{1+ 3a^{4}}\geq \frac{3}{4}$
$\frac{a}{1+ 3b^{4}}+ \frac{b}{1+ 3c^{4}}+ \frac{c}{1+ 3a^{4}}\geq \frac{3}{4}$
Started By dai101001000, 30-03-2018 - 18:53
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Posted 30-03-2018 - 21:55
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$\sum{\frac{a}{1+3b^4}}=\sum{a}-\sum{\frac{3ab^4}{1+b^4+b^4+b^4}}\geqslant 3-\frac{3}{4}(\sum{ab})\geqslant 3-\frac{9}{4}=\frac{3}{4}$
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Posted 01-04-2018 - 15:21
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