If x2 - 11x + 1 = 0, what is the value of x8 - 14159x4 + 11?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 10.
Given, x2 - 11x + 1 = 0
⇒ x + 1/x = 11
Squarying both sides,
⇒ x2 + 1/x2 + 2 = 121
⇒ x2 + 1/x2 = 119
Again squarying both sides,
x4 + 1/x4 + 2 = 14161
⇒ x4 + 1/x4 = 14159
According to the given expression,
x8 - 14159x4 + 11
⇒ x8 - (x4 + 1/x4)x4 + 11
⇒ x8 - x8 - 1 + 11 = 10