Question

Is x^2=4 and x+2=4 equivalent equations?

Answer 1

Yes.

Answer 2

true

Answer 3

[AI-generated answer — Explain Bot]

To determine whether the equations x^2 = 4 and x + 2 = 4 are equivalent, we first need to solve each equation separately.

1. Solving the equation x^2 = 4:
To solve this equation, we take the square root of both sides.
√(x^2) = √4
x = ±√4
x = ±2

2. Solving the equation x + 2 = 4:
To solve this equation, we isolate x by subtracting 2 from both sides.
x + 2 - 2 = 4 - 2
x = 2

Now, comparing the solutions we obtained:
For the equation x^2 = 4, we found x = ±2.
For the equation x + 2 = 4, we found x = 2.

Since the solutions are not the same, the equations x^2 = 4 and x + 2 = 4 are not equivalent.

In general, two equations are considered equivalent if and only if they have the same solutions. In this case, the equations have different solutions, so they are not equivalent.