Question

Which equations are true for x = –2 and x = 2? Select two options

Answer 1

Answer:

x^2 - 4 = 0

4x^2 = 16

Step-by-step explanation:

I literally took it, so I know it's correct

Answer 2

Complete Question:

Which equations are true for x = –2 and x = 2? Select two options

$x^{2}-4=0$

$x^{2}=-4$

$3 x^{2}+12=0$

$4 x^{2}=16$

$2(x-2)^{2}=0$

Answer:

The following equations are true for x = -2 and x = 2:

$x^{2}-4=0$

$4 x^{2}=16$

Step-by-step explanation:

Given ‘x’ values are – 2 and 2. To find which equation is true out of all given choices, we have to check the solution obtained from those equations are the same as given ‘x’ values.

Case A:

$x^{2}-4=0$

$x^{2}=4$

$x=\pm 2$ (Means x= - 2 and x = 2)

Case B:

$x^{2}=-4$

There is no solution for the above

Case C:

$3 x^{2}+12=0$

$3 x^{2}=-12$

$x^{2}=\frac{-12}{3}=-4$

There is no solution for the above

Case D:

$4 x^{2}=16$

$x^{2}=\frac{16}{4}$

$x^{2}=4$

$x=\pm 2$ (Means x= - 2 and x = 2)

Case E:

$2(x-2)^{2}=0$

$(x-2)^{2}=0$

$x^{2}-4 x+4=0$

where, $(a-b)^{2}=a^{2}-2 a b+b^{2}$

After factorisation, we get

(x – 2) (x – 2) = 0

x = 2 and x = 2

From all the above,  $x^{2}-4=0$ and $4 x^{2}=16$ are true.