Well, how we solve the puzzle from the previous post?
$ maple
License expires in 22 days
> solve([3*a*b-c*d=0,2*(a+b)-3*2*(c+d)=0, a>0, d>0]);
d (a - 3 d) 3 a (a - 3 d)
{b = -----------, c = -------------, 0 < a, 0 < d}
9 a - d 9 a - d
Let's verify it.
$ ginsh > a=1; d=1; 1 1 > b=(d*(a-3*d))/(9*a-d); -1/4 > c=(3*a*(a-3*d))/(9*a-d); -3/4
Ooops. But wait!
> a=1; d=10; 1 10 > b=(d*(a-3*d))/(9*a-d); 290 > c=(3*a*(a-3*d))/(9*a-d); 87 > (c*d)/(a*b); 3 > (2*(a+b))/(2*(c+d)); 3
So, (1, 290) and (10, 870) is one possible solution. But there are
infinitly many!