
Example: If x+1/x = 3, find the value of x^{3}+1/x^{3}. Solution: Given that, x+1/x = 3 Cubing on both sides, we get (x+1/x)^{3} = 3^{3} x^{3}+1/x^{3}+3.x.1/x.(x+1/x) = 27 x^{3}+1/x^{3}+3.3 = 27 x^{3}+1/x^{3}+9 = 27 x^{3}+1/x^{3} = 279 x^{3}+1/x^{3} = 18
Directions: Solve the following problems. 