COMC 2013 C Problem 2

(a) Determine all real solutions to a^{2}+10=a+10^{2}.

(b) Determine two positive real numbers a, b>0 such that a \neq b and a^{2}+b=b^{2}+a.

(c) Find all triples of real numbers (a, b, c) such that a^{2}+b^{2}+c=b^{2}+c^{2}+a=c^{2}+a^{2}+b.