Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. 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 hope our answers were useful. Return anytime for more information and answers to any other questions you have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
