solution of system of quadratic eqns



On 06/23/2012 07:14 AM, Aleksas Domarkas wrote:
> (%i1) eq1:x^2 + y^2 = 1$
> eq2:(x-0.5)^2+(y-0.5)^2=2$
>
> (%i3) solve([eq1,eq1-eq2]);
> rat: replaced -0.5 by -1/2 = -0.5
> rat: replaced -0.5 by -1/2 = -0.5
> (%o3) 
> [[y=-(sqrt(7)+1)/4,x=(sqrt(7)-1)/4],[y=(sqrt(7)-1)/4,x=-(sqrt(7)+1)/4]]
>
> Aleksas
>
>
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This works for me, also.

In solving the set, eq1 and (eq1-eq2), the quadratic terms, x^2 and y^2, 
drop out in the second equation. Hence, we are left with one quadratic 
equation and one linear one. Perhaps that simplification enables Maxima 
to solve the system. I would have thought Maxima to be capable of 
arriving at this point on its own though.

Krishna