Question

giúp bài 5

Answer 1

Bài 5:

a. Căn thức có nghĩa (CTCN) $\Leftrightarrow |x|-1\geq 0$

$\Leftrightarrow |x|\geq 1$

$\Leftrightarrow x^2\geq 1$

$\Leftrightarrow (x-1)(x+1)\geq 0\Leftrightarrow x\geq 1$ hoặc $x\leq -1$

b.

CTCN $\Leftrightarrow |x-1|-3\geq 0$

$\Leftrightarrow |x-1|\geq 3$

$\Leftrightarrow x-1\geq 3$ hoặc $x-1\leq -3$

$\Leftrightarrow x\geq 4$ hoặc $x\geq -2$

c.

CTCN $\Leftrightarrow 4-|x|\geq 0$

$\Leftrightarrow |x|\leq 4$

$\Leftrightarrow -4\leq x\leq 4$

 

 

Answer 2

d. CTCN \(\Leftrightarrow \left\{\begin{matrix} x-1\geq 0\\ x-2\sqrt{x-1}\geq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq 1\\ (\sqrt{x-1}-1)^2\geq 0\end{matrix}\right.\)

$\Leftrightarrow x\geq 1$

e.

CTCN $\Leftrightarrow 9-12x+4x^2>0$

$\Leftrightarrow (2x-3)^2>0$

$\Leftrightarrow 2x-3\neq 0\Leftrightarrow x\neq \frac{3}{2}$

f. CTCN \(\Leftrightarrow \left\{\begin{matrix} x-1\geq 0\\ x+2\sqrt{x-1}\neq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\geq 1\\ (\sqrt{x-1}+1)^2\neq 0\end{matrix}\right.\Leftrightarrow x\geq 1\)