Re: Ti92 solver [much simpler methods]
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Re: Ti92 solver [much simpler methods]
At 09:41 AM 11/04/98 -0500, RWW Taylor wrote:
>From "news.club-internet.fr" <agsd@CLUB-INTERNET.FR>:
>
>> I am trying this equation,
>> x+y=5
>> x2+y2 = 13
>> How can i write on the TI
>
>We haven't yet gotten to the situation of being able to
>just "punch the button" for an answer, and I don't think
>we ever will. You could issue a solve() command along
>with a "with" command (using |) here, but a bit of
>_analysis_ first is really helpful. Here's how I would
>tackle a system of equations like this on a TI-92:
>
>* Set up x+y=5 --> e1 and x^2+y^2 = 13 --> e2
> [Yes, the _equations_ are being stored as variables here.]
>
>* Take a logical first step by entering e1^2 - e2 --> e3 .
> The equation e3 displayed should be x*y = 12.
>
>* Now, put e2 - 2*e3 --> e4. The equation e4 is
> x^2 - 2x*y + y^2 = -11
>
>Notice that the left hand is the square of x-y, while the
>right hand side is -11. Obviously the solutions are going
>to be _complex_. You could continue on, on the TI-92, by
>taking the square root of e4 and solving along with e1, for
>a formal solution, or you could just state the results now
>by inspection. There will be two different solutions, but
>they are symmetric with respect to each other. With a little
>background in the theory of equations, you can state that
>the solutions are the roots of the equation W^2-5W-11 = 0.
or you just use your handy dandy 89 (or 92+) and type this:
solve(x+y=5 and x^2+y^2=13,{x,y})
to get it to spit out the answer:
x=3 and y=2 or x=2 and y=3
note that the AND has higher precedence than the OR, so (3,2) and (2,3) are
the solutions.
>
>This sort of "electronic blackboard" approach is how I have
>solved similar, tougher problems like the three-equation
>system x + y + z = 1, x^2 + y^2 + z^2 = 2, and
>x^3 + y^3 + z^3 = 3. And the four- or five-equation analogues
>of this system. It gets interesting.
how about:
solve(x+y+z=1 and x^2+y^2+z^2=2 and x^3+y^3+z^3=3,{x,y,z})
which gives:
false
which I have learned from my experience with TI calculators to mean that
this system has no solution.
>However, I'll bet others on this list have different, very
>possibly better, ideas...
of course. :>
oh wait, he asked for the 92. well, heres the simplest way to do it (i
have indented what the calculator displays after i press enter):
solve(x+y=5,y)
y=5-x
solve(x^2+y^2=13,x)|y=5-x
x=3 or x=2
solve(x+y=5,y)|x=3
y=2
solve(x+y=5,y)|x=2
y=3
which gives (3,2) and (2,3) as the solutions again.
you can also use simult( and rref( to solve systems of LINEAR (wont work
with this problem) equations, as noted on page 61 of the 89 manual and page
99 of the 92 manual.
--
Bill Risher Sparr UIN:1952775 ._, . . .
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