If x2 - 4x + 1 = 0, then what is the value of (x6 + x-6)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 2702
x2 - 4x + 1 = 0
⇒ x(x - 4) = -1
⇒ x + 1/x = 4
⇒ (x + 1/x)2 = 42
⇒ x2 + 1/x2 = 16 - 2 = 14
⇒ (x2 + 1/x2)3 = 143
⇒ x6 + 1/x6 + 3(x2 + 1/x2) = 2744
⇒ x6 + 1/x6 = 2744 - 42 = 2702