Correct Answer - Option 1 : -7
Given:
a2 + c2 + 17 = 2(a - 8b - 2b2)
calculation:
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 + c2 = 0
⇒ (a – 1)2 + (2b + 4)2 + c2 = 0
⇒ a = 1, b = -2 and c = 0
Now,
(a3 + b3 + c3) = (1)3 + (-2)3 + (0)3
⇒ 1 – 8 + 0
⇒ -7
∴ The required value is -7
