Re: Ti92 solver [Haste makes waste]
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Re: Ti92 solver [Haste makes waste]
Haste makes waste, as they say...
(and a bit of unwarranted overconfidence doesn't help).
> I am trying this equation,
> x+y=5
> x2+y2 = 13
> How can i write on the TI
There were more errors in that solution I posted this morning.
I really should have taken the time to actually run it through
my TI-89, instead of just describing the process:
> The equation e3 displayed should be x*y = 12.
The equation that actually _is_ displayed, of course, is 2x*y = 12,
which can be divided by 2 to give you x*y = 6 if you like.
Now when you subtract from e2 to get a perfect square you get
x^2 - 2x*y + y^2 = 1, which you can ask the calculator to _factor_
to get (x-y)^2 = 1 . You can then take a square root, and the
calculator displays |x-y| = 1 (which is the right way to take a
square root involving variables). No complex roots after all.
And of course, as I also suggested this morning, once you know the
value of x+y and x*y you can immediately write the polynomial equation
that has the solutions as its roots -- the corrected form of this equation
is x^2 - 5x + 6 = 0, with the obvious roots 2 and 3.
Certainly the use of the solver with "and", as suggested by Bill Risher, would
give you a quicker solution to this system of simultaneous equations. But of
course this particular set of equations is a "toy" set, created really to
foster some algebraic insight, and not needing a calculator to tackle. Hope
this isn't sounding like "sour grapes". :-)}
When you move up to more mysterious systems, you may well want to try to get
some insight into the nature and number of solutions for your system before
simple-mindedly grinding out an answer of some kind. Just because the
calculator tells you "false" you cannot conclude that there is no solution! In
fact that little system of three simultaneous equations I posted this AM can be
represented as the three roots of a certain cubic polynomial, and a solution
_does_ exist.
There are philosophical and pedagogical issues lurking here, as well as (I
suspect) the age-old conflict in perspective between the mathematician and the
engineer. One of the reasons I wanted to post an example of the method of
solving equations against each other is that I feel this is very closely
analogous to the rigorous kind of thinking that classical mathematics
represents. The fact is that this kind of rigorous thinking _can_ be pursued
(quite nicely, thank you) even if you have a calculator ready to take care of
all of the "messy details". As to whether it _should_ be pursued, I presume we
will continue to differ!
--- By the way, thanks also to Bill Risher for providing the other
suggested approaches to examining the problem at leisure. I
expect that it is going to take some time (and a lot of
creativity) before commonly-accepted _styles_ of work emerge
in this new medium.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
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