Question

if x+1/x=root 3 find the value of x^3+1/x^3

Answer 1

x + 1/x = root3

Take cube on both side

(x + 1/x)^3 = (root3)^3

x^3 + (1/x)^3 + 3 (x)^2 (1/x) + 3 (x)(1/x)^2 = 3root3

x^3 + 1/x^3 + 3x +3/x = 3root3

x^3 + 1/x^3 + 3 (x + 1/x) = 3root3

x^3 + 1/x^3 + 3 (root3) = 3root3

x^3 + 1/x^3 = 3root3 - 3root3

x^3 + 1/x^3 = 0