Question

Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0

Answer 1

The equation $x^{2} -4=0~~and~~4x^2=16$ are true for  x = -2 and x = 2.

The given equations are given as:

$x^2-4=0\\\\x^2=-4\\\\3x^2+12=0\\\\4x^2=16\\\\2(x-2)^2=0$

We need to select two equations that are true for x = -2 and x = 2.

What are the solutions to an equation ?

The solutions of an equation are the values that satisfy the given equation or make the equation true when substituted for unknowns in the equations.

Example:

x - 2 = 2

Here the solution for x - 2 = 2 is 4 because x = 4 will make the equation true.

4 - 2 = 2

2 = 2

Let's find the solutions for each equation.

1.

$x^2 - 4=0$

$x^{2}$ = 4

x = $\sqrt{4}$ = ± 2

x = = 2 and x = -2

2.

$x^2 =-4$

x = $\sqrt{-4}$

x = $\sqrt{-1 \times 4}$ = $\sqrt{-1}\times\sqrt{4}$

x = ± 2 $\sqrt{-1}$

x = 2i and x = -2i         where i = $\sqrt{-1}$

3.

3$x^{2}$ + 12  = 0

$x^{2}$ = -12 / 3 = -4

x = $\sqrt{-1}$ $\sqrt{4}$

x = ± 2$\sqrt{-1}$

x = 2i and x = -2i

4.

4$x^{2}$ = 16

$x^{2}$ = 16 / 4

$x^{2}$ = 4

x = $\sqrt{4}$

x = ±2

x = 2 and x = -2

5.

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

$(x-2)^2 = 0$

x - 2 = 0

x = 2.

Thus the equation $x^{2} -4=0~~and~~4x^2=16$ have solutions x = -2 and x = 2.

Learn more about solutions of equations here:

brainly.com/question/14506845

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