Given that x8 - 34x4 + 1 = 0, x> 0. What is the value of (x3 + x-3) ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 10√2
Concept
Given = x8 - 34x4 + 1 = 0
Dividing both sides by x4, we get
x4 + 1 / x4 = 34
Adding 2 to both sides, we get
(x2 + 1 / x2)2 = 36
Upon solving, we get
x2 + 1 / x2 = 6
Adding 2 to both sides
(x + 1 /x )2 = 8
= ( x + 1/x) = 2√2
Cubing Both Sides
x3 + 1 / x3 + 3 (x) ( 1/x) ( x + 1 /x) = 16√2
x3 + 1 / x3 + 3(2√2) = 16√2
x3 + 1 / x3 + 6(√2) = 16√2
x3 + 1 / x3 = 10√2