IMO 1995

Algebra Level 2

Q=1a3(b+c)+1b3(a+c)+1c3(a+b)Q=\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}

Let a,b,a,b, and cc be positive numbers such that abc=1abc = 1 .

What is the minimum value of the above expression?

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