Multiple choice

The roots of equation $(x \, - \, 1)^3 \, + \, 8 \, = \, 0$ are $ -1, \,1 \, - \, 2 \omega, \, 1 \, - \, 2 \omega^2$.True or False ?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(x - 1)^3 = -8. Taking the cube root, x - 1 = -2, -2w, -2w^2. Thus, x = 1 - 2, 1 - 2w, 1 - 2w^2, which are -1, 1 - 2w, 1 - 2w^2.

AI explanation

Rewrite the equation (x - 1)^3 + 8 = 0 as (x - 1)^3 = -8. Taking the cube root of both sides gives x - 1 = -2, -2 * omega, and -2 * omega^2. Adding 1 to each term gives x = -1, 1 - 2 * omega, and 1 - 2 * omega^2, so the statement is True.

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