35. (3) Solve the system of equations in real numbers:

$a^{2}+b^{2}=2 c, \quad 1+a^{2}=2 a c, \quad c^{2}=a b$.
Solution: Multiply the last equation by 2, add all the equations, and move everything to the left side. We will have: $(a-b)^{2}+(a-c)^{2}+(c-1)^{2}=0$. From this, we have $a=b=c=1$, which is the only solution.