Đáp án:
\(\max P = 1 \Leftrightarrow x = 0\)
Giải thích các bước giải:
\(\begin{array}{l}
\quad P = \left(1 + \dfrac{x + \sqrt x}{\sqrt x + 1}\right)\cdot\left(1 - \dfrac{ x - \sqrt x}{\sqrt x - 1}\right)\qquad (ĐKXĐ: x \geqslant 0;\ x \ne 1)\\
\to P = \left[1 + \dfrac{\sqrt x(\sqrt x + 1)}{\sqrt x + 1)}\right]\cdot \left[1 - \dfrac{\sqrt x(\sqrt x - 1)}{\sqrt x - 1}\right]\\
\to P = \left(1 + \sqrt x\right).\left(1 - \sqrt x\right)\\
\to P = 1 - x\\
\text{Ta có:}\\
\quad x \geqslant 0\\
\to - x \leqslant 0\\
\to 1 - x \leqslant 1\\
\text{Dấu = xảy ra}\ \Leftrightarrow x =0\\
Vậy\ \max P = 1 \Leftrightarrow x = 0
\end{array}\)
