Question

x+1/x= root 3, then find x^3+1/x^3

Answer 1

Given:

x + 1/x = √3

To find out:

Find the value of x³ + 1/x³.

Formula used:

( a + b )³ = a³ + b³ + 3( a + b )

Solution:

x + 1/x = √3

Cubing both sides

( x + 1/x )³ = (√3)³

➠ x³ + 1/x³ + 3 ( x + 1/x ) = 3√3

➠ x³ + 1/x³ + 3 × √3 = 3√3

➠ x³ + 1/x³ + 3√3 = 3√3

➠ x³ + 1/x³ = 3√3 - 3√3

➠ x³ + 1/x³ = 0