Question

if x^3+x/x^3=18 then the value of x+1/x is

Answer 1

  x³  + 1    = 18

           x³

(x + 1/x)³ = x³ + 1/x³ + 3(x+1/x)

let x + 1/x = a

so a ³ = x³ + 1/x³ + 3a

a³  = 18 + 3a

a³ - 3a  - 18 = 0

Let a = 3

27 - 9 - 18 = 0

So (a - 3) is a factor

Now divide a³ - 3a - 18 with (a - 3) will get (a² + 3a + 6)

So a³ - 3a - 18 = (a - 3) (a² + 3a + 6)

a- 3 = x + 1/x  - 3

x + 1/x = 3