@Carl Love 

Of course, calculated solutions are the all solutions. I meant that the code itself can be different. 

@Carl Love 

You wrote "The step length AD must be a multiple of primorial(n) where n is the progression length".  This is not true.

The example:   7, 157, 307, 457, 607, 757, 907

@Carl Love 

You wrote "The step length AD must be a multiple of primorial(n) where n is the progression length".  This is not true.

The example:   7, 157, 307, 457, 607, 757, 907

Why  AD=210 ?  What is the justification for?  It is obvious only that the difference of the progression  should be an even.

Why  AD=210 ?  What is the justification for?  It is obvious only that the difference of the progression  should be an even.

Mathematics is both a tool and an art, and that's fine.

@Markiyan Hirnyk 

Thank you!
You are right.  I did not notice that in the third quarter the plots are superimposed on one another. But Maple is also wrong, the solutions  {a=0, b=0}  and  {a=1, b=1}  are lost.

@Markiyan Hirnyk 

Thank you!
You are right.  I did not notice that in the third quarter the plots are superimposed on one another. But Maple is also wrong, the solutions  {a=0, b=0}  and  {a=1, b=1}  are lost.

@Markiyan Hirnyk

Try  RealDomain:-solve(sys, symbolic=false);

@Markiyan Hirnyk

Try  RealDomain:-solve(sys, symbolic=false);

@Markiyan Hirnyk 

Take a closer look:

sys := [sqrt(sin(x)^2+1/sin(x)^2)+sqrt(cos(y)^2+1/cos(y)^2) = sqrt(20*y/(x+y)), sqrt(sin(y)^2+1/sin(y)^2)+sqrt(cos(x)^2+1/cos(x)^2) = sqrt(20*x/(x+y))]:

A := lhs(sys[1])+lhs(sys[2]);

@Markiyan Hirnyk 

Take a closer look:

sys := [sqrt(sin(x)^2+1/sin(x)^2)+sqrt(cos(y)^2+1/cos(y)^2) = sqrt(20*y/(x+y)), sqrt(sin(y)^2+1/sin(y)^2)+sqrt(cos(x)^2+1/cos(x)^2) = sqrt(20*x/(x+y))]:

A := lhs(sys[1])+lhs(sys[2]);

st:=time(): Tuples(10, 4): time()-st;
                42.828

st:=time(): CartProdSeq([$0..4] $ 10): time()-st;
                46.593

@Markiyan Hirnyk

You are wrong on two points:

1. You forgot about the condition: acute triangle

2. This inequality requires symbolic, ie, the exact solution, rather than the approximate one.

@ThU 

You are right. Shoelace's formula is a wonderful formula! It is used in the text of the procedure  Area  for calculating the area of any region bounded non-selfintersecting line, if the whole or a part of the boundary is a broken line.

See  http://www.maplesoft.com/applications/view.aspx?SID=146470