Gbpt 1)(√2-√3)x
{4x-3.
_____ < x+3
2
2) {2 1
______
Gbpt 1)(√2-√3)x
{4x-3.
_____ < x+3
2
2) {2 1
______
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
\left( {\sqrt 2 – \sqrt 3 } \right)x \le \sqrt 3 + \sqrt 2 \\
\sqrt 2 – \sqrt 3 < 0 \Rightarrow x \ge \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 2 – \sqrt 3 }} \Leftrightarrow x \ge – 5 – 2\sqrt 6 \\
1,\\
\left\{ \begin{array}{l}
\left( {x – 3} \right)\left( {\sqrt 2 – x} \right) > 0\\
\frac{{4x – 3}}{2} < x + 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left( {x – 3} \right)\left( {x – \sqrt 2 } \right) < 0\\
2x – \frac{3}{2} < x + 3
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\sqrt 2 < x < 3\\
2x – x < 3 + \frac{3}{2}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\sqrt 2 < x < 3\\
x < \frac{9}{2}
\end{array} \right.\\
\Leftrightarrow \sqrt 2 < x < 3\\
\Rightarrow S = \left( {\sqrt 2 ;3} \right)\\
2,\\
\left\{ \begin{array}{l}
\frac{2}{{2x – 1}} \le \frac{1}{{3 – x}}\\
\left| x \right| < 1
\end{array} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( \begin{array}{l}
x \ne \frac{1}{2}\\
x \ne 3
\end{array} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{2}{{2x – 1}} – \frac{1}{{3 – x}} \le 0\\
\left| x \right| < 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{{2\left( {3 – x} \right) – \left( {2x – 1} \right)}}{{\left( {2x – 1} \right)\left( {3 – x} \right)}} \le 0\\
– 1 < x < 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{{7 – 4x}}{{\left( {2x – 1} \right)\left( {3 – x} \right)}} \le 0\\
– 1 < x < 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{{4x – 7}}{{\left( {2x – 1} \right)\left( {x – 3} \right)}} \le 0\\
– 1 < x < 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x < \frac{1}{2}\\
\frac{7}{4} \le x < 3
\end{array} \right.\\
– 1 < x < 1
\end{array} \right.\\
\Leftrightarrow – 1 < x < \frac{1}{2}\\
\Rightarrow S = \left( { – 1;\frac{1}{2}} \right)
\end{array}\)