Question

Tìm ĐKXĐ của các biểu thức :

a/ \(\frac{1}{\sqrt{2x-x^2}}\)

b/ \(\frac{1}{\sqrt{x-3}}+\frac{3x}{\sqrt{5-x}}\)

c/ \(\frac{1}{\sqrt{x^2-5x+6}}\)

d/ \(\sqrt{6x-1}+\sqrt{x+3}\)

Answer 1

a/ 2x-x²>0

\(\Leftrightarrow\) x(2-x)>0

\(\Leftrightarrow\) 0<x<2

b/ \(\left\{{}\begin{matrix}x-3>0\\5-x>0\end{matrix}\right.\)\(\Leftrightarrow\)\(\left\{{}\begin{matrix}x>3\\x< 5\end{matrix}\right.\)\(\Leftrightarrow\) 3<x<5

c/ x²-5x+6>0

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

\(\Leftrightarrow\) \(\left[{}\begin{matrix}x>3\\x< 2\end{matrix}\right.\)

d/ \(\left\{{}\begin{matrix}6x-1>0\\x+3>0\end{matrix}\right.\)

\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x>\frac{1}{6}\\x>-3\end{matrix}\right.\)

\(\Leftrightarrow\) x > \(\frac{1}{6}\)