Help in algebra and manipulation of equations

Ryan$

Full Member
Joined
Jan 25, 2019
Messages
296
Hi guys! please I'm struggling that problem every day and I want to cut off that struggle totally.

lets assume I have equation like X^2+Y^2+Z^2=M^2 and didn't say anything about it, so it's in general.

afterwards we have conclude over specific case that case is satisfying the equation over specific parameter like Z=0 , then can I say that "specific case" is satisfying that equation: X^2+Y^2=M^2 ?! if so then why? I'm stuck in that struggle everyday, how we can assign specific parameter over specific case and then we say it's satisfying the general equation over specific parameter ! ?!
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
4,156
Please don't try to generalize your questions. Instead, give a specific problem that you are actually working on, so we can see the real conditions under which these questions arise. Ask your question about such a specific problem, so that we can tell exactly what reason there is for each claim.

Until you cooperate in this way, you will not get satisfactory answers.
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
5,046
Yes, if you have a "general equation" of the form \(\displaystyle X^2+ Y^2+ Z^2= M^2\), and Z=0, then, because Z=0, you can replace "Z" by "0" to get \(\displaystyle X^2+ Y^2+ 0^2= M^2\) which is \(\displaystyle X^2+ Y^2= M^2\). I'm not sure what you mean by "satisfying the general equation over specific parameter". Setting Z=0 changes the "general" equation to a less general equation. (I wouldn't say "specific" because X and Y can still be any value.)
 
Top