Question

x-1/x=5 find x2-1/x^2 and 1/x^3-x^3​

Answer 1

Given: x - 1/x = 5

To find:

• x² -1/x² = ?
• 1/x³ - x³ = ?

Solution :

Given, x - 1/x = 5

or, (x - 1/x)² = 5^2

or, (x + 1/x)² - 4 * x * 1/x = 25

or, (x + 1/x)² - 4 = 25

or, (x + 1/x)² = 29

or, x + 1/x = ± √29

∴ x² - 1/x²

= (x + 1/x) (x - 1/x)

= ± √29 * 5

= ± 5√29

and 1/x³ - x³

= - (x³ - 1/x³)

= - { (x - 1/x)³ - 3 * x * 1/x (x - 1/x) }

= - { 5³ - 3 (5) }

= - ( 125 - 15 )

= - 110