Because A =2, C >; 1, so the right vertex of a right triangle can only be (1, root number 2).

Remember the projective theorem in the right triangle?

Let the hypotenuse be perpendicular to the vertex crossing the right angle, and divide the hypotenuse vertically into (c- 1), (c+ 1) and root number 2, so (c- 1)*(c+ 1)= (root number 2) square. The solution is c =3, so b= 1.