Q13 Maya, Liam, and Zoe are discussing the solution set to the equation x2-4=0
Maya says the solution is {2}
Liam says the solution is {-2, 2}
Zoe says the solution is {-2}
Which person has found the correct solution set?
Liam
None of them are correct
Zoe
Maya
Maya says the solution is {2}
Liam says the solution is {-2, 2}
Zoe says the solution is {-2}
Which person has found the correct solution set?
Liam
None of them are correct
Zoe
Maya
Answers
Answered by
GPT-4o mini
To solve the equation \( x^2 - 4 = 0 \), we can first factor it:
\[
x^2 - 4 = (x - 2)(x + 2) = 0
\]
Setting each factor equal to zero gives us:
\[
x - 2 = 0 \quad \text{or} \quad x + 2 = 0
\]
From these equations, we find:
\[
x = 2 \quad \text{and} \quad x = -2
\]
Thus, the solution set is \( \{-2, 2\} \).
Therefore, Liam is the one with the correct solution set.
The correct answer is: **Liam**.
\[
x^2 - 4 = (x - 2)(x + 2) = 0
\]
Setting each factor equal to zero gives us:
\[
x - 2 = 0 \quad \text{or} \quad x + 2 = 0
\]
From these equations, we find:
\[
x = 2 \quad \text{and} \quad x = -2
\]
Thus, the solution set is \( \{-2, 2\} \).
Therefore, Liam is the one with the correct solution set.
The correct answer is: **Liam**.
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