Question

If x-1/x =√5 , then find the value of x³+1/x³​

Answer 1

Answer:

Step-by-step explanation:

x -1/x = √5

(x + 1/x)² = (x  - 1/x)² + 4

             = (√5)² + 4

              = 9

x + 1/x = √9 = ±3

we know that (a + b)³ = a³  + b³ + 3ab(a +b) => a³  + b³ = (a + b)³ - 3ab(a +b)  

if x + 1/x = + 3,

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

             = (3)³ - 3(3)

              = 18

if x + 1/x = - 3,

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

             = (-3)³ - 3(-3)

              = -18