Question
If a, b and c are integers such that a 3 + b
3 + c 3 = 192 + 3abc, ab + bc + ac = a 2 + b 2 + c 2 - 16, then what is the value of (a + b + c)?Solution
As we know, a 3 + b 3 + c 3 = (a + b + c)(a 2 + b 2 + c 2 - ab - bc - ac) + 3abc
Then, 192 + 3abc = (a + b + c)(a 2 + b 2 + c 2 - (a 2 + b 2 + c 2 - 16)) + 3abc
a + b + c = 12
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