Question

Answer 1

1.

a, ĐK: \(x\ge-1\)

\(\Leftrightarrow x+\sqrt{x+1}< 2+\sqrt{x+1}\)

\(\Leftrightarrow x< 2\)

\(\Rightarrow x\in[-1;2)\)

b, ĐK: \(x< \dfrac{1}{2}\)

\(\dfrac{2-x}{\sqrt{1-2x}}\le\dfrac{1}{\sqrt{1-2x}}\)

\(\Leftrightarrow2-x\le1\)

\(\Leftrightarrow x\ge1\)

\(\Rightarrow\) vô nghiệm

c, ĐK: \(x\le3\)

\(\left(x-1\right)\sqrt{3-x}\ge0\)

\(\Leftrightarrow x-1\ge0\)

\(\Leftrightarrow x\ge1\)

\(\Rightarrow x\in\left[1;3\right]\)

Answer 2

2.

ĐK: \(x\le1\)

\(\left(x-m\right)\sqrt{1-x}\ge0\)

\(\Leftrightarrow x-m\ge0\)

\(\Leftrightarrow m\le x\le1\)

Vậy \(m\le1\)