Fie \( a,\ b,\ c>0 \) a. i. \( a+b+c\ge\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \). Demonstrati ca \( \sum\frac{a^{3}c}{b\left(c+a\right)}\ge\frac{3}{2} \).
Cezar Lupu, lista scurta, 2005
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