Multiple choice

The roots of the equation $\displaystyle x^{2/3}+x^{1/3}-2=0$ 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 y = x^(1/3). The equation becomes y^2 + y - 2 = 0. Factoring gives (y+2)(y-1) = 0, so y = 1 or y = -2. If x^(1/3) = 1, x = 1. If x^(1/3) = -2, x = -8.

AI explanation

Let y equal x^(1/3), which allows the equation to be rewritten as the quadratic y^2 + y - 2 = 0. Factoring this quadratic gives (y + 2)(y - 1) = 0, so y equals -2 or 1. Substituting x^(1/3) back in for y gives x^(1/3) = -2 or x^(1/3) = 1. Cubing both sides of each equation yields the roots 1 and -8.

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