If a + b + c = 6, a2 + b2 + c2 = 30 and a3 + b3 + c3 = 165, then the value of 2abc is?

2 1 4 3

2

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) (6)2 = 30 + 2(ab + bc + ca) 36 - 30 = 2(ab + bc + ca) (ab + bc + ca) = 3 Now, a3 + b3 + c3 - 3abc = (a + b + c) [a2 + b2 + c2 - (ab + bc + ca)] 165 - 3abc = 6 [30 - 3] 165 - 6(27) = 3abc 3abc = 165 - 162 = 3 abc = 1 Hence, 2abc = 2