If x + (1/x) = (√3 + 1)/2, then what is the value of x4 + 1/x4?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. (–4√3 – 1)/4
x + 1/x = (√3 + 1)/4
On squaring both sides,
x2 + 1/x2 + 2 = (4 + 2√3)/4
x2 + 1/x2 = (2 + √3)/2 - 2 = [√3 - 2/2]
Again squaring both sides,
x4+ 1/x4 = (–4√3 – 1)/4