Question

if x + 1/x = 3 . FIND (1.) x^2 + 1/x^2 (2.)x - 1/x (3.)x^2 - 1/x^2 (4.)x^3 + 1/x^3​

Answer 1

Step-by-step explanation:

x + 1/x = 3

(1) x² + 1/x² = (x + 1/x)² - 2. x .1/x = (3)² - 2 = 9 - 2 = 7

(2) (x - 1/x)² = (x + 1/x)² - 4.x.1/x = (3)² - 4 = 9 - 4 = 5

=> x - 1/x = √5

(3) x² - 1/x² = (x + 1/x) (x - 1/x) = 3√5

(4) x³ + 1/x³ = (x + 1/x)³ - 3.x.1/x (x + 1/x)

=> (3)³ - 3 . 3 = 27 - 9 = 18