Answer:
•4x^2 = 16
•2(x - 2)^2 = 0
Step-by-step explanation:
To solve this problem, we can simply substitute x = -2 and x = 2 into each of the given equations, and see which ones are true.
Let's start with x = -2:
x^2 - 4 = 0: (-2)^2 - 4 = 0, so this equation is not true for x = -2.
x^2 = -4: (-2)^2 = 4, which is not equal to -4, so this equation is not true for x = -2.
3x^2 + 12 = 0: 3(-2)^2 + 12 = 12, which is not equal to 0, so this equation is not true for x = -2.
4x^2 = 16: 4(-2)^2 = 16, so this equation is true for x = -2.
2(x - 2)^2 = 0: 2(-2 - 2)^2 = 0, so this equation is true for x = -2.
Now let's try x = 2:
x^2 - 4 = 0: 2^2 - 4 = 0, so this equation is not true for x = 2.
x^2 = -4: 2^2 = 4, which is not equal to -4, so this equation is not true for x = 2.
3x^2 + 12 = 0: 3(2)^2 + 12 = 36, which is not equal to 0, so this equation is not true for x = 2.
4x^2 = 16: 4(2)^2 = 16, so this equation is true for x = 2.
2(x - 2)^2 = 0: 2(2 - 2)^2 = 0, so this equation is true for x = 2.
Therefore, the two equations that are true for both x = -2 and x = 2 are:
4x^2 = 16
2(x - 2)^2 = 0
In summary, by substituting x = -2 and x = 2 into each equation and checking for equality, we found the two equations that are true for both values of x.