Question

If x + 1/x = 5, find the value of x^3 + 1/x^3

Answer 1

110

Explanation:

The expansion (a + b)³ is

(a + b)³ = a³ + b³ + 3ab(a + b)

Then

(x +
`(1)/(x)` )³ with a = x and b =
`(1)/(x)`

= x³ +
`(1)/(x^3)` + 3x .
`(1)/(x)` (x +
`(1)/(x)` )

Thus

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

= 5³ - 3(5)

= 125 - 15

= 110

Answer 2

x=5/3 your answer right answer