Question

multiple and simplify (x^1/3 + x^-1/3)^2

Answer 1

(x^1/3 + x^-1/3)^2

using (a + b)^2 = a^2 + 2ab + b^2 we get
= (x^1/3)^2 + 2(x^1/3)(x^-1/3) + (x^-1/3)^2
= x^1/3*2 + 2[x^1/3+(-1/3)] + x^-1/3*2
= x^2/3 + 2[x^0] + x^-2/3
= x^2/3 + 2 + x^-2/3

Answer 2

Set cube root of x = y then

(y+1/y)^2 = y^2 + 1/y^2 + 2 sub back adding exponents as per last question

x^2/3 + 2 + x^-2/3