Question

x+1/x =-1 prove that x^3 equal to 1

Answer 1

Answer:

x³ = 1 Proved.

Step-by-step explanation:

Given :

x + 1 / x = - 1

⇒ x² + 1 = - x

⇒ x² + x + 1 = 0

Now we know :

x³ - 1³  = ( x + 1 ) ( x² + x + 1 )

Putting value of  ( x² + x + 1 ) = 0

x³ - 1³  = ( x + 1 ) × 0

x³ - 1³  = 0

x³ = 1

Hence proved.

Answer 2

Step-by-step explanation:

Given :

x + 1 / x = - 1

⇒ x² + 1 = - x

⇒ x² + x + 1 = 0

Now we know :

x³ - 1³  = ( x + 1 ) ( x² + x + 1 )

Putting value of  ( x² + x + 1 ) = 0

x³ - 1³  = ( x + 1 ) × 0

x³ - 1³  = 0

x³ = 1

Hence proved.