Đáp án:
$1)\\a) 0 <x<\dfrac{2}{3} \\b) 3<x<10\\c)-2 <x<2, x \ne 0.$
Giải thích các bước giải:
$1)\\ D=x^2-\dfrac{2}{3}x<0\\ \Leftrightarrow x\left(x-\dfrac{2}{3}\right)<0\\ \Leftrightarrow \left[\begin{array}{l} \left\{\begin{array}{l} x>0 \\x-\dfrac{2}{3} <0 \end{array} \right.\\ \left\{\begin{array}{l} x<0 \\x-\dfrac{2}{3} >0 \end{array} \right.\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} \left\{\begin{array}{l} x>0 \\x<\dfrac{2}{3} \end{array} \right.\\ \left\{\begin{array}{l} x<0 \\x>\dfrac{2}{3} \end{array} \right.(\text{Vô lí})\end{array} \right.\\ \Leftrightarrow 0 <x<\dfrac{2}{3} \\ E=\dfrac{x-3}{x-10}<0\\ \Leftrightarrow \left[\begin{array}{l} \left\{\begin{array}{l} x-3>0 \\x-10<0 \end{array} \right.\\ \left\{\begin{array}{l} x-3<0 \\x-10>0 \end{array} \right.\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} \left\{\begin{array}{l} x>3 \\x<10 \end{array} \right.\\ \left\{\begin{array}{l} x<3 \\x>10 \end{array} \right.(\text{Vô lí})\end{array} \right.\\ \Leftrightarrow 3<x<10\\ F=\dfrac{x^2-4}{x^2}(x \ne 0)\\ \text{Do } x^2>0 \ \forall \ x \ne 0\\ F<0 \Leftrightarrow x^2-4<0\\ \Leftrightarrow x^2-2x+2x-4<0\\ \Leftrightarrow x(x-2)+2(x-2)<0\\ \Leftrightarrow (x+2)(x-2)<0\\ \Leftrightarrow \left[\begin{array}{l} \left\{\begin{array}{l} x+2>0 \\x-2<0 \end{array} \right.\\ \left\{\begin{array}{l} x+2<0 \\x-2>0 \end{array} \right.\end{array} \right.\\ \Leftrightarrow \left[\begin{array}{l} \left\{\begin{array}{l} x>-2 \\x<2 \end{array} \right.\\ \left\{\begin{array}{l} x<-2 \\x>2 \end{array} \right.(\text{Vô lí})\end{array} \right.\\ \Leftrightarrow -2 <x<2$
Kết hợp điều kiện $\Rightarrow -2 <x<2, x \ne 0.$
