On Sep 28, 10:33 am, "Bruno Luong" <b.lu...@fogale.findmycountry>
wrote:
> "Peter Schreiber" <schreiber.pete...@gmail.com> wrote in message <j5taqi$bs...@newscl01ah.mathworks.com>...
> > Hello,
> > How would I go about solving an implicit equation like..
>
> > sqrt(a*x^2+b*x+c)+sqrt(d*x^2+e*x+f)=g
>
> > a,b,c,d,e,f,g are real constants and I would like to find x (which is a real quantity too) that solves the equation.
>
> Let
> P(x) := a*x^2+b*x+c
> Q(x) := d*x^2+e*x+f.
>
> The above equation is:
>
> sqrt(P(x))+sqrt(Q(x))=g
>
> => P(x) + Q(x) + sqrt(P(x)*Q(x)) = g^2
> => P(x)*Q(x) = [g^2  P(x) + Q(x)]^2
> => [g^2  P(x) + Q(x)]^2  P(x)*Q(x) = 0
>
> The latest equation is a quartic polynomial equation that can be solved numerically with ROOTS command. A close form solutions also exist.
>
> Bruno
Uh, oh, Bruno, you've missed a 2 factor in the cross product.
(a+b)^2=a^2 + 2ab +b^2
