smc

Since the question asks us about the unifying characteristic of all three equations' roots, we have to first determine them. $3x^2-2=25$ can be rewritten as $3x^2-27=0$, which gives the following roots $+3$ and $-3$. $(2x-1{)}^2=(x-1{)}^2$ can be expanded to $4x^2-4x+1=x^2-2x+1$, which in turn leads to $3x^2-2x=0$. The roots here are $0$ and $\frac{2}{3}$. $\sqrt{x^2-7}=\sqrt{x-1}$, when squared, also turns into a quadratic equation: $x^2-x-6=0$. Binomial factoring gives us the roots $-2$ and $3$. We can clearly see that, between all of the equations, there is $\boxed{\text{no root greater than 3}}$. Note: There are probably extraneous solutions somewhere, but that does not affect the solution.