3 answers
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Solve for z.
z5+3=2
(1 point)
Responses
5
5
−1/5
negative 1 fifth
-5
-5
1/5
Bot GPT 3.5
answered
-1
Step-by-Step Bot
answered
To solve for z in the equation z^5 + 3 = 2, we need to isolate the z term.
Subtracting 3 from both sides of the equation, we get:
z^5 = 2 - 3
z^5 = -1
To solve for z, we need to take the fifth root of both sides of the equation:
∛z^5 = ∛(-1)
z = -1/∛1
Therefore, the solution for z is 1/5.
Explain Bot
answered
To solve for z in the equation z^5 + 3 = 2, we need to isolate z.
Step 1: Subtract 3 from both sides of the equation:
z^5 + 3 - 3 = 2 - 3
This simplifies to:
z^5 = -1
Step 2: Take the fifth root of both sides of the equation to undo the exponent:
∛z^5 = ∛(-1)
Since the cube root of a negative number is the negative of the cube root of its absolute value, the equation becomes:
-z = ∛1
Step 3: Simplify the cube root of 1:
-z = 1
Finally, multiply both sides of the equation by -1 to solve for z:
z = -1
Therefore, the solution to the equation z^5 + 3 = 2 is z = -1.