Classical

Algebra Level 3

1a3(b+c)+1b3(a+c)+1c3(a+b)\large \dfrac{1}{a^3(b+c)}+\dfrac{1}{b^3(a+c)}+\dfrac{1}{c^3(a+b)}

Let aa, bb, and cc be positive real numbers such that abc=1abc=1, then find the minimum value of the expression above.

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