$$\frac{a^3}{a^3+(b+c)^3}+\frac{b^3}{b^3+(a+c)^3}+\frac{c^3}{c^3+(b+a)^3}+1>2(\frac{a^2}{a^2+(b+c)^2}+\frac{b^2}{b^2+(a+c)^2}+\frac{c^2}{c^2+(b+c)^2})$$
Edited by doxuantung97, 24-02-2013 - 14:42.
CMR: $\sum \frac{a^3}{a^3+(b+c)^3}+1 \geq 2\sum \frac{a^2}{a^2+(b+c)^2}$
Started By Math Is Love, 24-02-2013 - 14:40
#1
Posted 24-02-2013 - 14:40
Math Is Love
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$\mathfrak{Forever}\ \mathfrak{Love}$
Cho $a,b,c$ là độ dài ba cạnh của một tam giác.Chứng minh rằng:
$$\frac{a^3}{a^3+(b+c)^3}+\frac{b^3}{b^3+(a+c)^3}+\frac{c^3}{c^3+(b+a)^3}+1>2(\frac{a^2}{a^2+(b+c)^2}+\frac{b^2}{b^2+(a+c)^2}+\frac{c^2}{c^2+(b+c)^2})$$
$$\frac{a^3}{a^3+(b+c)^3}+\frac{b^3}{b^3+(a+c)^3}+\frac{c^3}{c^3+(b+a)^3}+1>2(\frac{a^2}{a^2+(b+c)^2}+\frac{b^2}{b^2+(a+c)^2}+\frac{c^2}{c^2+(b+c)^2})$$
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