\(M=P+Q=3x^2y-2x+5xy^2-7y^2+3xy^2-7y^2-9x^2y-x-5=-6x^2y+8xy^2-3x-7y^2-5\)

\(M=Q-P=3xy^2-7y^2-9x^2y-x-5-\left(3x^2y-2x+5xy^2-7y^2\right)=-12x^2y-2xy^2+x-5\)

\(3;\) \(x\in Z;P\in Z?\)

\(\Rightarrow\dfrac{-1}{\sqrt{x}-3}\in Z\Leftrightarrow\sqrt{x}-3\inƯ\left(1\right)=\left(\pm1\right)\Leftrightarrow x=\left\{16;4\right\}\)

\(đkxđ:x\ge0;x\ne9;x\ne4\Rightarrow x=16\left(tm\right)\)

\(\Rightarrow x^2+y^2=9-z^2\ge0\Leftrightarrow-3\le z\le3\)

\(\Rightarrow P=\dfrac{x+z-1}{y+4}\ge\dfrac{x-3-1}{y+4}=\dfrac{x-4}{y+4}=\dfrac{3+z-y-4}{y+4}=\dfrac{-y+z-1}{y+4}\ge\dfrac{-y-3-1}{y+4}=\dfrac{-\left(y+4\right)}{y+4}=-1\)

dấu"=" xảy ra \(\Leftrightarrow x=y=0;z=-3\)