be u,v natural numbers without common divisor and x,y,z natural numbers each smaller or equal to u*v.

now, prove that it is possible to determine x,y,z in such a way that

0 < sqrt(y² - 4xz) =< 2x/(uv).

well, i have been trying to solve this all night but only could do so applying certain constraints (e.g. that 2 is a factor of either u or v). could anybody help me find a general solution to this?

thanks