Tìm x, biết: a, $\frac{x-2}{x-6}$ < 0 b, $x^{2}$ + 4x > 0

0 bình luận về “Tìm x, biết: a, $\frac{x-2}{x-6}$ < 0 b, $x^{2}$ + 4x > 0”

1. Đáp án:

   $\begin{array}{l}
   a)\dfrac{{x – 2}}{{x – 6}} < 0\\
    \Rightarrow \left[ \begin{array}{l}
   \left\{ \begin{array}{l}
   x – 2 > 0\\
   x – 6 < 0
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x – 2 < 0\\
   x – 6 > 0
   \end{array} \right.
   \end{array} \right. \Rightarrow \left[ \begin{array}{l}
   \left\{ \begin{array}{l}
   x > 2\\
   x < 6
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x < 2\\
   x > 6
   \end{array} \right.\left( {ktm} \right)
   \end{array} \right.\\
    \Rightarrow 2 < x < 6\\
   \text{Vậy}\,2 < x < 6\\
   b){x^2} + 4x > 0\\
    \Rightarrow x\left( {x + 4} \right) > 0\\
    \Rightarrow \left[ \begin{array}{l}
   \left\{ \begin{array}{l}
   x > 0\\
   x + 4 > 0
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x < 0\\
   x + 4 < 0
   \end{array} \right.
   \end{array} \right. \Rightarrow \left[ \begin{array}{l}
   \left\{ \begin{array}{l}
   x > 0\\
   x >  – 4
   \end{array} \right.\\
   \left\{ \begin{array}{l}
   x < 0\\
   x <  – 4
   \end{array} \right.
   \end{array} \right.\\
    \Rightarrow \left[ \begin{array}{l}
   x > 0\\
   x <  – 4
   \end{array} \right.\\
   \text{Vậy}\,x > 0\,\text{hoặc}\,x <  – 4
   \end{array}$

   Bình luận