@Kitonum Thank you very much.

@Carl Love Thank you very much. 

@Markiyan Hirnyk In your opinion, is there one solution (n = 12) or two solutions (n = 12 and n = 11)?

@Markiyan Hirnyk I think, if my quetion is find n so that only a8 max, then n = 12. 

@Carl Love Thank you very much.

@Carl Love I only want to know, the given equation has one or two solutions when I solve in RealDomain?

I don't understand your line add(C[k]*t[k], k= 1..nops(C)); not receive P (see your picture).

@Carl Love Thank you very much.

@Carl Love If I only want real solutions. How must I do?

@Carl Love How to eval in this code?

restart:
n:=expand((x*a+y*b+z*c)*b):
eval(n,[a*b=1, b*c=4, b^2=4]);

@Markiyan Hirnyk I am sorry. I used simplify@expand(sqrt(p*(p-a)*(p-b)*(p-c))); 

@Markiyan Hirnyk It does not work. I got `@`(simplify,1/576*523^(1/2)*576^(1/2))

At here http://mathematica.stackexchange.com/questions/39994/find-the-centre-of-findgeometrictransform have a problem. Your code can solve that problem?

@Kitonum How can I search the triangles in list L with three givent sides? For example 17, 28, 39. 

@Kitonum How can I get it?