Given

A^2=B^2, C^2=D^2

......does (A+C)^2=(B+D)^2?

I got down to this

AC=BD

I then divived both sides by "A"

C=BD/A

My proof goes as following....

It is possible that B=A.....eg A=6....B=6.....A^2=B^2.......36=36

So if this is possible. this equation breaks down to

C=D.... However it is clear that C is not always equal to D

Can anyone recommend a better proof?

Thankyou