Question 3
a) Solve
$$\begin{cases}(2x+3)\sqrt{4x-1}+(2y+3)\sqrt{4y-1}=2\sqrt{(2x+3)(2y+3)},\\x+y=4xy.\end{cases}$$
b) Let $x,y,z\gt 1$ satisfy $x+y+z=\dfrac43xyz$. Find the minimum of
$$P=\frac{y-2}{x^2}+\frac{z-2}{y^2}+\frac{x-2}{z^2}.$$
$$\begin{cases}(2x+3)\sqrt{4x-1}+(2y+3)\sqrt{4y-1}=2\sqrt{(2x+3)(2y+3)},\\x+y=4xy.\end{cases}$$
b) Let $x,y,z\gt 1$ satisfy $x+y+z=\dfrac43xyz$. Find the minimum of
$$P=\frac{y-2}{x^2}+\frac{z-2}{y^2}+\frac{x-2}{z^2}.$$