Question

If (x)^(1/3) + (1/x)^(1/3)= 3 then x^3 + (1/x)^3 = ?

Answer 1

(x)^(1/3) + (1/x)^(1/3)= 3 ----- A
[ cubing both sides using (a + b)^3 = a^3 + b^3 + 3(a^2)(b) + 3(a)(b^2) ]

x + (1/x) + 3*[(x)^(1/3) + (1/x)^(1/3)] = 27
From A [(x)^(1/3) + (1/x)^(1/3)] = 3

x + (1/x) + 3*3 = 27
x = [9 + (4*(5^(1/2)))] & [9 - (4*(5^(1/2)))]
therefore

x^3 + (1/x)^3 = 5778.