Question

Which equation are true for x=-2 and x=2 check all that apply

Answer 1

1 it is true

`{x}^(2) - 4 = 0 \\ {x}^(2) = + 4 \\ x = √(4) = 2`
2 it's not true

`{x}^(2) = - 4`
3 it's not true

`3 {x}^(2) + 12 = 0 \\ 3 {x}^(2) = - 12 \\ {x}^(2) = ( - 12)/(3) = - 4 \\`
4 it's true

`4 {x}^(2) = 16 \\ {x}^(2) = (16)/(4) = 4 \\ x = √(4) = 2`
5- it's true

`{2(x - 2)}^(2) = 0 \\ {(x - 2)}^(2) = 0 \\ x - 2 = 0 \\ x = 2`

Answer 2

A.
`x^2-4=0`

D.
`4x^2=16`

Explanation:

To check which of the given equations have solution
`x=-2\text{ and }x=2`, we will solve our given equations one by one.

A.
`x^2-4=0`

`x^2-4+4=0+4`

`x^2=4`

`√(x^2)=\pm√(4)`

`x=\pm 2`

`x=-2\text{ or }x=2`

Therefore, option A is the correct choice.

B.
`x^2=-4`

To solve our given equation, we need to take square root of both sides of equation. Since square root is not defined for negative numbers, therefore, option B is not a correct choice.

C.
`3x^2+12=0`

`3x^2=-12`

`x^2=-4`

To solve our given equation, we need to take square root of both sides of equation. Since square root is not defined for negative numbers, therefore, option C is not a correct choice.

D.
`4x^2=16`

`x^2=4`

`√(x^2)=\pm√(4)`

`x=\pm 2`

`x=-2\text{ or }x=2`

Therefore, option D is the correct choice.

E.
`2(x-2)^2=0`

`(x-2)^2=0`

`√((x-2)^2)=√(0)`

`x-2=0`

`x=2`

Therefore, option E is not a correct choice.