Select the correct answer. What are the values of x in this equation? 'x^ (2/5) + x^ (1/5) + 1 = 3' A. 32, - 1 B. 32, 1 C. - 32, 1 D. - 32, - 1

x^ (2/5) + x^ (1/5) + 1 = 3

subtract 3 from each side

x^ (2/5) + x^ (1/5) - 2=0

let m = x^1/5

m^2 + m - 2 = 0

(m - 1) (m + 2) = 0

using the zero product property

m=1 m=-2

replace m = x^1/5

x^1/5 = 1 and x^1/5 = - 2

take everything to the 5th powr

x^ 1/5 ^ 5 = 1^5 and x^ 1/5 ^ 5 = - 2 ^ 5

x = 1 and x = - 32

Choice C

C. - 32, 1