Let a,b and c be ration numbers and b=12/5-13/5a,c=13/5-12/5

-c=-1/5-1/5a=-1/5(1+a) b+c=5-5a=5(1-a)
a^2-b^2+c^2
=a^2-(b^2-c^2)
=a^2-(b-c)(b+c)
=a^2-[-1/5(1+a)]×5(1-a)
=a^2+(1+a)(1-a)
=a^2+1-a^2
=1