Min Value of 1/6 (a^3 + b^3 + c^3 - 3abc) for Distinct Ints

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NEILS BOHR
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Homework Statement


If a , b ,c r distinct +ve integers such that ab + bc + ca is greater than equal to 107 , then find the minimum value of 1/6 ( a^3 + b^3 + c^3 - 3abc )


Homework Equations





The Attempt at a Solution


tried usin AM GM equality but i m confused which nos. shud i use??
 
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Discussion

NEILS BOHR said:
got the ans finally using AM GM only...:biggrin:
Can you show me?... i got stuck too. XD
 

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