Giải bất phương trình sau :
a)$\left| {2x^{2}-3x-15} \right|\leq -2x^{2}-8x-6$
b)$\left| {\frac{10x^{2}-3x-2}{x^{2}-3x+2}} \right| >1$
c)$\sqrt{x^{2}-5x+4}\leq 2x+2$ 
a. Ta có:
       $|2x^2-3x-15|\le-2x^2-8x-6$
$\Leftrightarrow \left\{\begin{array}{l}2x^2-3x-15\le-2x^2-8x-6\\-2x^2+3x+15\le-2x^2-8x-6\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}4x^2+5x-9\le0\\11x+21\le0\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}\dfrac{-9}{4}\le x\le 1\\x\le\dfrac{-21}{11}\end{array}\right.\Leftrightarrow \dfrac{-9}{4}\le x\le\dfrac{-21}{11}$
c. Điều kiện: $x^2-5x+4\ge0 \Leftrightarrow \left[\begin{array}{l}x\le1\\x\ge4\end{array}\right.$
BPT đã cho tương đương với:
     $\sqrt{x^2-5x+4}\le2x+2$
$\Leftrightarrow \left\{\begin{array}{l}2x+2\ge0\\x^2-5x+4\le4x^2+8x+4\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x\ge-1\\3x^2+13x\ge0\end{array}\right.$
$\Leftrightarrow x\ge0$
Kết hợp với điều kiện ta có: $x\in[0;1]\cup[4;+\infty)$
bạn ơi bạn giải dùm mình câu b luôn được không vậy bạn ! –  leesoohee97qn 01-05-13 04:13 PM
Câu b) Bình phương hai vế  ( điều kiện x $\neq  1 và   x \neq  2$)
$\left| {\frac{10x^2 - 3x - 2}{x^2 - 3x + 2}} \right|^2 >1$
<=> $(\frac{10x^2 - 3x - 2 }{x^2 -3x +2} - 1 ) ( \frac{10x^2 - 3x -2}{x^2 - 3x + 2} +1) > 0$
<=> $\frac{9x^2 - 4}{x^2 - 3x + 2} \times  \frac{11x^2 - 6x}{x^2 - 3x + 2} > 0$
Lập bảng xét dấu : 
      $-\infty $              -2/3            0               6/11               2/3                 1               2          $+\infty $
f(x)               +                  -                 +                   -                    +       ||        +    ||       +
Vậy S = ( $-\infty , -2/3)  \bigcup  ( 0 ,   6/11) \bigcup  ( 2/3 ,  +\infty )  $ \ { 1, 2 }

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