Question 25
It is given that $a,b,c$ are positive integers such that the roots of the three quadratic equations
$$x^2-2ax+b=0,\qquad x^2-2bx+c=0,\qquad x^2-2cx+a=0$$
are all positive integers. Determine the maximum value of $abc$.
$$x^2-2ax+b=0,\qquad x^2-2bx+c=0,\qquad x^2-2cx+a=0$$
are all positive integers. Determine the maximum value of $abc$.