Question

please solve this question ​

Answer 1

x + 1/x = 5

squaring. both sides we get,

x² + 1/x² + 2 × x × 1/x = 25

=> x² + 1/x² + 2 = 25

=> x² + 1/x² = 23______________1

now square x - 1/x

=> (x - 1/x)² = x² + 1/x² - 2 × x × 1/x

=> (x - 1/x)² = x² + 1/x² - 2

=> (x - 1/x)² = 23 - 2 [ from 1 (x² + 1/x²) = 23

=> (x - 1/x)² = 21

taking square root on both sides,

=> x - 1/x = √21 Answer