A89: Re: Re: Re: Re: Re: C question... actually two C questions...
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A89: Re: Re: Re: Re: Re: C question... actually two C questions...
Hi!
> I _THINK_ that you'll only create a possible extraneous
> root if either the numerator or denominator is even,
> because that's the only time you have to worry about
> positive and negative bases giving the same result when
> raised to the power. In other words, if we had a^3=b^3,
> I think we could make the assumption that a=b - but I'll
> leave that to others here to confirm of refuse.
Yes, this is for TI-Math, but I need some elaboration on
it. This is true only if we assume the set of real numbers.
a^n=b^n implies a=b if n is an odd number. But, in the set
of complex numbers, this is not true. For example,
a=2, b=-1+i*sqrt(3)
Then a^3=b^3 (you can check it on TI), but a!=b...
Now, the more general case, a^n=b^n. Assume that a is
fixed. If n is integer, there is exactly n various
possibilities for b (in the set of complex number) such
that this equation is true. The situation is even worse
if n is rational. And, if n is irrational, there exist
an infinity number of different pairs (a,b) for which
a^n=b^n, but the most two of them may be consist of
real numbers.
Cheers,
Zeljko Juric
P.S. If somebody has some advanced math question, he can
try to ask me using my private mail: I am quite good in
mathematics...