Simple Inequality 3

Algebra Level 3

\(a,b\) and \(c\) are three positive real numbers such that \(a+b+c=n\).

What is the smallest possible value of \(n\) such that \[(ab+bc+ca)\left(\dfrac{a}{2b+3c}+\dfrac{b}{2c+3a}+\dfrac{c}{2a+3b}\right)\ge 20\] for all possible ordered triplets \((a,b,c)\)?

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