If x4 + x-4 = 194, x > 0, then the value of x + is :
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 4
x4 + x-4 = 194
(a + b)2 = a2 + b2 + 2ab
x4 + 1/x4 = 194
On adding 2 on both sides -
x4 + 1/x4 + 2 = 196
(x2 + 1/x2)2 = (14)2
x2 + 1/x2 = 14
On adding 2 on both sides -
x2 + 1/x2 + 2 = 16
(x + 1/x)2 = 16
x + 1/x = 4