Question

If x = `1/[ 5 - x ]  "and x ≠ 5 find "x^3 + 1/x^3`

Answer 1

Given x = `1/[ 5 - x ]`;

By cross multiplication

⇒ x(5 - x) = 1

⇒ x² - 5x = -1

⇒ x² + 1 = 5x

⇒ `[ x^2 + 1]/x = 5`

⇒ `[ x + 1/x ] = 5`           ...(1)

We know that

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

= `(5)^3 - 3(5)`                     ...[From equation (1)]

= `x^3 + 1/x^3`

= 125 - 15

= 110