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Thế là chị thì k dc làm ak? :-?
Bài 4:
$\sqrt{x(m+2) + m} > |x - 1|$
\Leftrightarrow $mx + 2x + m > x^2 - 2x + 1$
\Leftrightarrow $(x+1)m > x^2 - 4x + 1$
\Leftrightarrow $m > \dfrac{x^2 - 4x + 1}{x + 1}$ (do $x \in [0;2]$) (1)
Đặt: $f(x) = \dfrac{x^2 - 4x + 1}{x + 1}$ \Rightarrow (1) \Leftrightarrow m > f(x)
$f'(x) = \dfrac{x^2 + 2x - 5}{(x+1)^2}$
Kẻ BBT ra nhé cậu! 
Từ BBT \Rightarrow m > 1.