Q414
If a + b + c = 8 and ab + bc + ca = 12, then a3 + b3 + c3 - 3abc is equal to:
A.
192
B.
224
AnswerC.
144
D.
400
Answer: Option B
Solution
Answer: Option B
Solution:
a + b + c = 8 and ab + bc + ca = 12a3 + b3 + c3 - 3abc = ?
Let c = 0
a + b = 8, ab = 12
a3 + b3 = (a + b)(a2 + b2 - ab)
a3 + b3 = (a + b)[(a + b)2 - 3ab]
a3 + b3 = 8[82 - 3 × 12]
a3 + b3 = 224