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# Inequality 45(Vo Quoc Ba Can)

Problem:

Let $\displaystyle a,b,c$ be positive real numbers such that $\displaystyle ab+bc+ca=1$. Prove that $\displaystyle \frac{1}{\sqrt{1+(2a-b)^2}}+\frac{1}{\sqrt{1+(2b-c)^2}}+\frac{1}{\sqrt{1+(2c-a)^2}}\leq\frac{3\sqrt{3}}{2}$.