Q367
If a + b = 8 and a + a2b + b + ab2 = 128 then the positive value of a3 + b3 is:
A.
96
B.
224
C.
344
D.
152
AnswerAnswer: Option D
Solution
Answer: Option D
Solution:
a + b = 8a + a2b + b + ab2 = 128
(a + b) + ab(a + b) = 128
(1 + ab)(a + b) = 128
1 + ab = 16
ab = 15
a3 + b3
= (a + b)3 - 3ab(a + b)
= 512 - 3 × 15 × 8
= 512 - 360
= 152