if a + b + c = 6, a2 + b2 + c2 = 32, and a3 + b3 + c3 = 189, then the value of 4abc is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 12
We know, (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac)
⇒ 2(ab + bc + ac) = 36 - 32 = 4
⇒ (ab + bc + ac) = 4/2 = 2
We know, (a + b + c)(a2 + b2 + c2 - (ab + bc + ac)) = a3 + b3 + c3 - 3abc
⇒ 6 × (32 - 2) = 189 - 3abc
⇒ 3abc = 189 - 180 = 9
⇒ abc = 3
Thus, 4abc = 12