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Inequality 26(Vasile Cirtoaje)

Problem:

Let \displaystyle a,b,c be non-negative real numbers. Prove that \displaystyle \frac{a}{2a^2+bc}+\frac{b}{2b^2+ca}+\frac{c}{2c^2+ab}\geq \frac{a+b+c}{a^2+b^2+c^2}.


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