Arithmetic mean and geometric mean

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Homework Statement

Arithmetic mean and geometric mean

Relevant Equations

Arithmetic mean and geometric mean

If a, b, and c are positive real numbers and a² + b² + c² = 3, what is the minimum value of the expression [1/(1+ab)] + [1/(1+bc)] + [1+(1+ac )]?

Usage: A² + B² + C² ≥ AB+AC+BC

Answer: 3/2

 

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PS. Your "Usage" statement for general A, B, C could be stronger.