If x4 - 79x2 + 1 = 0, then a value of x + x-1 can be:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 9
x4 - 79x2 + 1 = 0
(x + 1/x)2 = x2 + 1/x2 + 2
x4 - 79x2 + 1 = 0
Divide by x2 we get -
x2 - 79 + 1/x2 = 0
x2 + 1/x2 = 79
x2 + 1/x2 + 2 = 79 + 2
(x + 1/x)2 = 81
x + 1/x = 9
Now, x + x-1 = x + 1/x
x + x-1 = 9