solve for Z
z^3 = -9 where z is a real number
I think that there is no solution. Is this correct?
No. z=-1 is a solution.
To solve for Z in the equation z^3 = -9, you can use the concept of taking the cube root of both sides of the equation. Here's how you can do it step by step:
Step 1: Recognize the given equation: z^3 = -9
Step 2: Take the cube root of both sides to isolate z. The cube root of -9 is written as ∛(-9) or (-9)^(1/3). Taking the cube root of a negative number will result in a real number.
Step 3: Calculate the cube root of -9: ∛(-9) ≈ -2.08
Step 4: So, the real solution for z is approximately z = -2.08.
Note: Since the equation has only one real solution, there are no other values for z that satisfy the equation z^3 = -9.