Answer :
To solve the equation [tex]\(x^2 = 9\)[/tex], we need to determine the values of [tex]\(x\)[/tex] that make this equation true. Here's how you can approach this:
1. Understand the Equation: The equation [tex]\(x^2 = 9\)[/tex] means you are looking for all values of [tex]\(x\)[/tex] whose square equals 9.
2. Finding Solutions:
- A key property of squares is that a positive number has two square roots: one positive and one negative.
- So, to find the values of [tex]\(x\)[/tex], consider that:
- [tex]\(x\)[/tex] can be [tex]\(\sqrt{9}\)[/tex], which equals 3.
- [tex]\(x\)[/tex] can also be [tex]\(-\sqrt{9}\)[/tex], which equals -3.
3. List the Solutions: From this, we find:
- The first solution is [tex]\(x = 3\)[/tex].
- The second solution is [tex]\(x = -3\)[/tex].
Therefore, the solutions to the equation [tex]\(x^2 = 9\)[/tex] are [tex]\(x = 3\)[/tex] and [tex]\(x = -3\)[/tex].
Now we can match these solutions with the given options:
- C. 3 is correct.
- D. -3 is correct.
The other options don't match the solutions:
- A. 0, B. 81, E. -81 do not satisfy [tex]\(x^2 = 9\)[/tex].
- F. None is incorrect because we do have solutions.
So, the correct options to check are C and D.
1. Understand the Equation: The equation [tex]\(x^2 = 9\)[/tex] means you are looking for all values of [tex]\(x\)[/tex] whose square equals 9.
2. Finding Solutions:
- A key property of squares is that a positive number has two square roots: one positive and one negative.
- So, to find the values of [tex]\(x\)[/tex], consider that:
- [tex]\(x\)[/tex] can be [tex]\(\sqrt{9}\)[/tex], which equals 3.
- [tex]\(x\)[/tex] can also be [tex]\(-\sqrt{9}\)[/tex], which equals -3.
3. List the Solutions: From this, we find:
- The first solution is [tex]\(x = 3\)[/tex].
- The second solution is [tex]\(x = -3\)[/tex].
Therefore, the solutions to the equation [tex]\(x^2 = 9\)[/tex] are [tex]\(x = 3\)[/tex] and [tex]\(x = -3\)[/tex].
Now we can match these solutions with the given options:
- C. 3 is correct.
- D. -3 is correct.
The other options don't match the solutions:
- A. 0, B. 81, E. -81 do not satisfy [tex]\(x^2 = 9\)[/tex].
- F. None is incorrect because we do have solutions.
So, the correct options to check are C and D.
