Can the equation x^3=−217 yield a positive final solution? Why or why not?
No, because all cubed numbers yield negative solutions.
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.
The correct answer is:
Yes, because cubed roots can give two solutions.
While it is true that cubing a negative number will yield a negative result, it is also true that the equation x^3=−217 can have two different solutions: one positive and one negative. When you take the cube root of both sides of the equation, you will find both solutions.
Yes, because cubed roots can give two solutions.
The correct answer is "Yes, because cubed roots can give two solutions." Now, let me explain how to arrive at this answer.
To determine if the equation x^3 = -217 can yield a positive final solution, we need to consider the properties of cubic equations and roots.
A cubic equation has the form of ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are constants.
In this case, the equation is x^3 = -217, which can be rewritten as x^3 + 217 = 0.
To find the roots of this equation, we can use the concept of cubed roots. The cubed root of a number is a value that, when raised to the power of 3, gives the original number.
Since we want to find a positive final solution, we need to determine if any of the cubed roots of -217 are positive. It's important to note that the cubed root can have both positive and negative solutions.
To find the cubed root of -217, we can use a scientific calculator or an online calculator that supports complex number calculations. The cubed root of -217 is approximately -6.24264 + 3.09656i, where i is the imaginary unit.
So, since the cubed root of -217 is a complex number with an imaginary component, it does not yield a positive final solution.
Therefore, the correct answer is "No, because cubed roots can give two solutions."