If a + b = 8 and a +a2b + b + ab2 = 128 then the positive value of a3 + b3 is:
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Correct answer: D
Explanation
The correct answer is option 4 i.e 152
Given that,
⇒ a +a2b + b + ab2 = 128
⇒ a(1 + ab) + b(1 + ab) = 128
⇒ (a + b)(1 + ab) = 128
⇒ (1 + ab) = 128 / 8 = 16 (a + b = 8)
⇒ ab = 15
By factorization: a = 3 / 5, b = 5 / 3
⇒ a3 + b3 = (5)3 + (3)3 = 125 + 27 = 152