absolute value equations

[bananasbasket]

the question is: solve for x in | x + 2 | = |y^2 - 4|

i started out with the squaring trick so it would be easier because listing down all the cases would be tedious. what’s the next step after squaring both sides? thank you[MATH][/MATH]

 

[Cubist]

The next step is to make it look like a quadratic in x.

Please post back with your working

 

[Steven G]

I would look at the cases. There are not that many.

 

[bananasbasket]

how can i exactly do that, given that there’s y variables on the left side of the equation?

The next step is to make it look like a quadratic in x.

Please post back with your working

 

[Steven G]

You get two cases.

One property of absolute values is if | A | = | B |, then either A = B or A = -B. Can you prove this theorem??

x + 2 = y^2 - 4 OR -(x + 2) = y^2 - 4