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Question 113
If a, b, c be all positive integers, then the least positive value of $$a^{3} + b^{3} + c^{3} - 3abc$$ is
Solution
$$a^{3} + b^{3} + c^{3} - 3abc$$ = (a+b+c)($$(a^2 + b^2 + c^2)$$ - ab -bc-ac)
we will get minimum value when a=b=c as all are positive so the minimum value is 0
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