Hi!
I need help understanding this answer. Because x is being raised to an odd power, doesn’t that mean it’d result in the absolute value of x? Which isn’t equal to x, so the answer would be can’t be determined? I’m confused on why it’d result in a positive regardless of what x equals (this is written in the solution)
That’s not what the solution is saying:
The cube root of x^3 is always x, no matter whether x is positve or not.
In other words, it’s saying that no matter what x is, the two quantities are equal.
how it this different from another quiz question that had the square root of x^2 and quantity A and X as quantity B. And the answer was can’t be determined because quantity A resulted in the absolute value of x
Because 2 is even. \sqrt{x^2} is indeed |x|, because the square root of something cannot be negative (which is not the case for \sqrt[3]{x^3}).
so aren’t we saying the same thing? 3rd root of x to the third = x and the square root of x squared = absolute value of x ?
And if that’s the case, I don’t follow why the answer to the quiz question is can’t be determined if 3rd root of x to the third = x
That is true.
Are you sure the answer to the quiz is D and not C?
