Question
If a 3 + b 3 + c 3 =
62, abc = -6 and (a + b + c) = 5, then what is the value of ab + bc + ac?Solution
We know, (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ac
5 2 = a 2 + b 2 + c 2 + 2(ab + bc + ac)
a 2 + b 2 + c 2 = 25 - 2(ab + bc + ac))...(i)
a 3 + b 3 + c 3 = (a + b + c)(a 2 + b 2 + c 2 - ab - bc - ac) + 3abc
62 = 5 * (25 - 2(ab + bc + ac) - (ab + bc + ac)) + 3 * (-6) (from (i))
ab + bc + ac = 3
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