I read this well written article [ https://www.nctm.org/tmf/library/drmath/view/72802.html ] by drp
What is the domain issue?
Then he says
eg : if 4=4 then sqrt(4)=sqrt(4) -> 2=2
or
if sqrt(4)=sqrt(4) then a = b i.e 4=4
I did not ignore anything but still proved both equivalent then what he is saying by ignoring domain issues?
One or both may be negative means ? suppose there are two nos -4=-4 (both are negative) then i cannot take square root of both the numbers as they will be extended to complex no but why did he said one may be negative the equation with one negative be like this 4 =-4 (which is not valid in the first place) .The only thing that could go wrong, really, is if
you can't perform the operation at all (e.g. if you want to take the
square root of both sides but one or both may be negative). This
becomes a domain issue, if you are familiar with functions
What is the domain issue?
Then he says
What does this mean?you just have to
determine that it is well-defined (has one value) and that its domain
includes the values to which it is being applied
These 2 equations are equivalent from both sides .Although it is true that
lthough it is true that
if a = b, then sqrt(a) = sqrt(b), and in fact these equations are
equivalent if you ignore domain issues
eg : if 4=4 then sqrt(4)=sqrt(4) -> 2=2
or
if sqrt(4)=sqrt(4) then a = b i.e 4=4
I did not ignore anything but still proved both equivalent then what he is saying by ignoring domain issues?
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