Đáp án: x>1 Giải thích các bước giải: \(\begin{array}{l}\sqrt P < P\\ \to P – \sqrt P > 0\\ \to \sqrt P \left( {\sqrt P – 1} \right) > 0\\ \to \left\{ \begin{array}{l}\sqrt P – 1 > 0\\\sqrt P \ne 0\end{array} \right.\left( {do:\sqrt P > 0\forall P \ne 0} \right)\\ \to \left\{ \begin{array}{l}P > 1\\P \ne 0\end{array} \right.\\ \to \left\{ \begin{array}{l}\dfrac{{\sqrt x }}{{\sqrt x – 1}} > 1\\\dfrac{{\sqrt x }}{{\sqrt x – 1}} \ne 0\end{array} \right.\\ \to \left\{ \begin{array}{l}\dfrac{{\sqrt x – \sqrt x + 1}}{{\sqrt x – 1}} > 0\\x \ne 0;x \ne 1;x \ge 0\end{array} \right.\\ \to \dfrac{1}{{\sqrt x – 1}} > 0\\ \to \sqrt x – 1 > 0\\ \to x > 1\end{array}\) Bình luận
Đáp án:
x>1
Giải thích các bước giải:
\(\begin{array}{l}
\sqrt P < P\\
\to P – \sqrt P > 0\\
\to \sqrt P \left( {\sqrt P – 1} \right) > 0\\
\to \left\{ \begin{array}{l}
\sqrt P – 1 > 0\\
\sqrt P \ne 0
\end{array} \right.\left( {do:\sqrt P > 0\forall P \ne 0} \right)\\
\to \left\{ \begin{array}{l}
P > 1\\
P \ne 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{\sqrt x }}{{\sqrt x – 1}} > 1\\
\dfrac{{\sqrt x }}{{\sqrt x – 1}} \ne 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{\sqrt x – \sqrt x + 1}}{{\sqrt x – 1}} > 0\\
x \ne 0;x \ne 1;x \ge 0
\end{array} \right.\\
\to \dfrac{1}{{\sqrt x – 1}} > 0\\
\to \sqrt x – 1 > 0\\
\to x > 1
\end{array}\)