1: Khi x=16 thì \(N=\dfrac{\sqrt{16}-3}{2\cdot\sqrt{16}-16}=\dfrac{4-3}{2\cdot4-16}=\dfrac{1}{-8}=-\dfrac{1}{8}\)
2: \(M=\dfrac{2+\sqrt{x}}{2-\sqrt{x}}-\dfrac{2-\sqrt{x}}{2+\sqrt{x}}-\dfrac{4x}{x-4}\)
\(=\dfrac{-\left(\sqrt{x}+2\right)}{\sqrt{x}-2}+\dfrac{\sqrt{x}-2}{\sqrt{x}+2}-\dfrac{4x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{-\left(\sqrt{x}+2\right)^2+\left(\sqrt{x}-2\right)^2-4x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{-x-4\sqrt{x}-4+x-4\sqrt{x}+4-4x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{-4x-8\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=-\dfrac{4\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=-\dfrac{4\sqrt{x}}{\sqrt{x}-2}\)
3: P=M:N
\(=-\dfrac{4\sqrt{x}}{\sqrt{x}-2}:\dfrac{\sqrt{x}-3}{2\sqrt{x}-x}\)
\(=\dfrac{4\sqrt{x}}{\sqrt{x}-2}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{\sqrt{x}-3}=\dfrac{4\sqrt{x}}{\sqrt{x}-3}\)
Để |P|=1 thì \(\left[{}\begin{matrix}P=1\\P=-1\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\dfrac{4\sqrt{x}}{\sqrt{x}-3}=1\\\dfrac{4\sqrt{x}}{\sqrt{x}-3}=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4\sqrt{x}=\sqrt{x}-3\\4\sqrt{x}=-\sqrt{x}+3\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}3\sqrt{x}=-3\\5\sqrt{x}=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=-1\left(nhận\right)\\\sqrt{x}=\dfrac{3}{5}\end{matrix}\right.\)
=>x=9/25(nhận)
