Question

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

Answer 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