Multiple choice

The roots of the equation $x^\frac{2}{3} + x^\frac{1}{3} - 2 = 0$, are

  1. $1, 4$
  2. $1, -4$
  3. $1, -8$
  4. $1, 8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u = x^(1/3). The equation becomes u^2 + u - 2 = 0. Factoring gives (u+2)(u-1) = 0, so u = 1 or u = -2. If x^(1/3) = 1, then x = 1. If x^(1/3) = -2, then x = (-2)^3 = -8.

AI explanation

Substitute y = x^(1/3) into the equation to get y^2 + y - 2 = 0. Factoring the quadratic gives (y-1)(y+2) = 0, meaning y = 1 or y = -2. Replacing y with x^(1/3) results in x^(1/3) = 1 or x^(1/3) = -2, which yields x = 1 or x = -8.

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