what inference can we draw from an equation which says that sum of two square numbers is zero? I have an equation $(a-2b)^2 + (b-2c)^2 = 0$ where, $a$, $b$ and $c$ are positive real numbers. What will be $a:b:c$?

For any real number $x$ we have $x^2\ge 0$, thus it follows that $a-2b=b-2c=0.$ Can you take it from here?
