If 2x − 1/(2x) = 10/3 and x > 1, then find the value of (x² + 1/(16x²)).
Show answer & explanation
Correct answer: B
Explanation
Given:
2x − 1/(2x) = 10/3, x > 1
Using the formula:
(a − b)² = a² + b² − 2ab
(2x − 1/(2x))² = (10/3)²
4x² + 1/(4x²) − 2 = 100/9
4x² + 1/(4x²) = 100/9 + 2 = 118/9
x² + 1/(16x²) = 118/36 = 59/18