Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Sure, let's examine each equation with the given values [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex] to determine which of them hold true.
1. Equation: [tex]\( x^2 - 4 = 0 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ (-2)^2 - 4 = 4 - 4 = 0 \][/tex]
So, the equation is true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2^2 - 4 = 4 - 4 = 0 \][/tex]
So, the equation is also true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( x^2 - 4 = 0 \)[/tex] is true for both [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex].
2. Equation: [tex]\( x^2 = -4 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ (-2)^2 = 4 \neq -4 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2^2 = 4 \neq -4 \][/tex]
So, the equation is also not true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( x^2 = -4 \)[/tex] is not true for either [tex]\( x = -2 \)[/tex] or [tex]\( x = 2 \)[/tex].
3. Equation: [tex]\( 3x^2 + 12 = 0 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ 3(-2)^2 + 12 = 3 \cdot 4 + 12 = 12 + 12 = 24 \neq 0 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 3 \cdot 2^2 + 12 = 3 \cdot 4 + 12 = 12 + 12 = 24 \neq 0 \][/tex]
So, the equation is also not true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( 3x^2 + 12 = 0 \)[/tex] is not true for either [tex]\( x = -2 \)[/tex] or [tex]\( x = 2 \)[/tex].
4. Equation: [tex]\( 4x^2 = 16 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ 4(-2)^2 = 4 \cdot 4 = 16 \][/tex]
So, the equation is true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 4 \cdot 2^2 = 4 \cdot 4 = 16 \][/tex]
So, the equation is also true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( 4x^2 = 16 \)[/tex] is true for both [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex].
5. Equation: [tex]\( 2(x-2)^2 = 0 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ 2(-2-2)^2 = 2(-4)^2 = 2 \cdot 16 = 32 \neq 0 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2(2-2)^2 = 2 \cdot 0 = 0 \][/tex]
So, the equation is true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( 2(x-2)^2 = 0 \)[/tex] is true only for [tex]\( x = 2 \)[/tex].
The equations that are true for the given values [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex] are:
- [tex]\( x^2 - 4 = 0 \)[/tex]
- [tex]\( 4x^2 = 16 \)[/tex]
- [tex]\( 2(x-2)^2 = 0 \)[/tex]
Hence, the correct options are:
- [tex]\( x^2 - 4 = 0 \)[/tex]
- [tex]\( 4x^2 = 16 \)[/tex]
- [tex]\( 2(x-2)^2 = 0 \)[/tex]
1. Equation: [tex]\( x^2 - 4 = 0 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ (-2)^2 - 4 = 4 - 4 = 0 \][/tex]
So, the equation is true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2^2 - 4 = 4 - 4 = 0 \][/tex]
So, the equation is also true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( x^2 - 4 = 0 \)[/tex] is true for both [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex].
2. Equation: [tex]\( x^2 = -4 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ (-2)^2 = 4 \neq -4 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2^2 = 4 \neq -4 \][/tex]
So, the equation is also not true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( x^2 = -4 \)[/tex] is not true for either [tex]\( x = -2 \)[/tex] or [tex]\( x = 2 \)[/tex].
3. Equation: [tex]\( 3x^2 + 12 = 0 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ 3(-2)^2 + 12 = 3 \cdot 4 + 12 = 12 + 12 = 24 \neq 0 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 3 \cdot 2^2 + 12 = 3 \cdot 4 + 12 = 12 + 12 = 24 \neq 0 \][/tex]
So, the equation is also not true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( 3x^2 + 12 = 0 \)[/tex] is not true for either [tex]\( x = -2 \)[/tex] or [tex]\( x = 2 \)[/tex].
4. Equation: [tex]\( 4x^2 = 16 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ 4(-2)^2 = 4 \cdot 4 = 16 \][/tex]
So, the equation is true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 4 \cdot 2^2 = 4 \cdot 4 = 16 \][/tex]
So, the equation is also true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( 4x^2 = 16 \)[/tex] is true for both [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex].
5. Equation: [tex]\( 2(x-2)^2 = 0 \)[/tex]
For [tex]\( x = -2 \)[/tex]:
[tex]\[ 2(-2-2)^2 = 2(-4)^2 = 2 \cdot 16 = 32 \neq 0 \][/tex]
So, the equation is not true for [tex]\( x = -2 \)[/tex].
For [tex]\( x = 2 \)[/tex]:
[tex]\[ 2(2-2)^2 = 2 \cdot 0 = 0 \][/tex]
So, the equation is true for [tex]\( x = 2 \)[/tex].
Therefore, [tex]\( 2(x-2)^2 = 0 \)[/tex] is true only for [tex]\( x = 2 \)[/tex].
The equations that are true for the given values [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex] are:
- [tex]\( x^2 - 4 = 0 \)[/tex]
- [tex]\( 4x^2 = 16 \)[/tex]
- [tex]\( 2(x-2)^2 = 0 \)[/tex]
Hence, the correct options are:
- [tex]\( x^2 - 4 = 0 \)[/tex]
- [tex]\( 4x^2 = 16 \)[/tex]
- [tex]\( 2(x-2)^2 = 0 \)[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.