Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive 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 appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
