Đáp án:
\(\min P = - \dfrac14 \Leftrightarrow x = \dfrac94\)
Giải thích các bước giải:
\(\begin{array}{l}
\quad P = A(x - \sqrt x -2)\\
\to P = \dfrac{\sqrt x - 1}{\sqrt x+1}\cdot \left(x - \sqrt x - 2\right)\\
\to P = \dfrac{\sqrt x - 1}{\sqrt x + 1}\cdot \left(\sqrt x +1\right)\left(\sqrt x - 2\right)\\
\to P = \left(\sqrt x - 1\right)\left(\sqrt x - 2\right)\\
\to P = x - 3\sqrt x + 2\\
\to P = x - 2\cdot \dfrac32\cdot \sqrt x + \dfrac94 - \dfrac14\\
\to P = \left(\sqrt x - \dfrac32\right)^2 - \dfrac14\\
\to P \geqslant - \dfrac14\\
\text{Dấu = xảy ra}\ \Leftrightarrow \sqrt x - \dfrac32 = 0 \Leftrightarrow x = \dfrac94\\
\text{Vậy}\ \min P = - \dfrac14 \Leftrightarrow x = \dfrac94
\end{array}\)
