Simple Inequality 3

Algebra Level 4

If $$a,b,c$$ 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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