If a + b + c = 6, a2 + b2 + c2 = 30 and a3 + b3 + c3 = 165, then the value of 2abc is?
Answer & explanation
Correct answer: option 1
(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