If $a^2+c^2+17=2\left(a-8 b-2 b^2\right)$, then what is the value of $\left(a^3+b^3+c^3\right)$ ?
Answer & explanation
Correct answer: option 1
According to the question,
a2 + c2 + 17 = 2(a - 8b - 2b2)
a2 + c2 + 17 = 2(a - 8b - 2b2)
= a2 + c2 + 17 = 2a – 16b – 4b2
= a2 + 4b2 + c2 + 17 = 2(a – 8b)
= a2 – 2a + 1 + 4b2 + 16b + 16 + c2 = 0
= (a – 1)2 + (2b + 4)2 + c2 = 0
= a = 1, b = -2 and c = 0
Put the values of a, b and c in (a3 + b3 + c3)
(a3 + b3 + c3) = (1)3 + (-2)3 + (0)3
= 1 – 8 + 0 = -7