If a + b = 8 and $a + a^2b + b + ab^2 = 128$ then the positive value of $a^3 + b^3$ is :
Answer & explanation
Correct answer: option 4
a + b = 8 and a + a2 b + b + ab2 = 128
We know that,
a3 + b3 = (a + b) [(a + b)2 - 3ab]
So,
a + a2 b + b + ab2 = 128
a + a2 b + b + ab2 = 128
= 8 + a2 b + ab2 = 128
= a2 b + ab2 = 128 - 8
= a2 b + ab2 = 120
= ab (a + b) = 120
= ab × 8 = 120
= ab = 15
a3 + b3 = (a + b) [(a + b)2 - 3ab]
= a3 + b3 = 8 [82 - 3 × 15]
= a3 + b3 = 8 [64 - 45]
= a3 + b3 = 8 × 19
a3 + b3 = 152