Question

x+1/x=3 find x^3+1/x^3

Answer 1

Given x+1/x = 3

Required= x^3 + 1/x^3

we know that.

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

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

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

substituting info

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

27 - 9 = (x)^3 + (1/x)^3

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