Correct Answer - Option 3 : 52
Given:
t2 – 4t + 1 = 0
Formula used:
(a + b)3 = a3 + b3 + 3ab(a + b)
Calculation:
Given expression is t2 – 4t + 1 = 0
⇒ t2 + 1 = 4t
⇒ t + 1/t = 4 ----(1)
Now, Taking cube both side
(t + 1/t)3 = 43
⇒ t3 + 1/t3 + 3(t × 1/t)(t + 1/t) = 64
⇒ t3 + 1/t3 + 3(t + 1/t) = 64
⇒ t3 + 1/t3 + 3 × 4 = 64 ----(From eq (1))
⇒ t3 + 1/t3 = 64 – 12
∴ t3 + 1/t3 = 52