Question

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?

Answer 1

To solve the equation \( x^2 - 4 = 0 \), we can rearrange it to:

\[
x^2 = 4
\]

Taking the square root of both sides gives:

\[
x = \pm 2
\]

This means the solutions are \( x = 2 \) and \( x = -2 \). Therefore, the solution set is:

\[
\{-2, 2\}
\]

Based on this analysis:

- Maya's solution of \{2\} is incorrect as it does not include -2.
- Liam's solution of \{-2, 2\} is correct as it includes both solutions.
- Zoe's solution of \{-2\} is incorrect as it does not include 2.

So, **Liam** has found the correct solution set.