Can the equation x3 = —217 yield a positive final solution? Why or why not?

Question

(1 point)
• No, because you must cube a negative number to get a negative answer.
• Yes, because multiplying three negatives together will equal a positive number.
• Yes, because cubed roots can give two solutions.
• No, because all cubed numbers yield negative solutions.

Answer 1

The correct response to the question is:

• No, because you must cube a negative number to get a negative answer.

To elaborate, when you cube a positive number, the result is positive. When you cube a negative number, the result is negative. Since the equation given is \( x^3 = -217 \), the only real solution for \( x \) would be a negative number, specifically \( x = -\sqrt[3]{217} \), which is negative. Thus, you cannot obtain a positive final solution from this equation.