Question

5. If 2(x^2 + 1) = 5x, find :
(i.) x - 1 / x
(ii.) x^3 - 1/x^3​

Answer 1

Step-by-step explanation:

x² + 1 = 5x/2

(x² + 1)/x = 5/2

x + 1/x = 5/2

x - 1/x = √(x + 1/x)² - 4

= √(5/2)² - 4

= √(25/4) - 4

= √(25-16)/4

= √(9/4)

= 3/2

(x - 1/x)³ = x³ - 1/x³ - 3(x - 1/x)

(3/2)³ = x³ - 1/x³ - 3(3/2)

then ,

x³ - 1/x³ = (27/8) + 9/2

= 27/8 + 36/8

= 63/8