Question

Các căn thức sau có nghĩa khi nào?

a, √(x²-8x-9)

b, √(2x-4/5-x)

Answer 1

a. \(\sqrt{x^2-8x-9}\) có nghĩa khi \(x^2-8x-9\ge0\)

\(\Leftrightarrow\left(x-9\right)\left(x+1\right)\ge0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\le-1\\x\ge9\end{matrix}\right.\)

b \(\sqrt{2x-\frac{4}{5-x}}\) có nghĩa khi \(\left\{{}\begin{matrix}x\ne5\\2x\left(5-x\right)-4\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne5\\10x-2x^2-4\ge0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ne5\\\frac{5-\sqrt{17}}{2}\le x\le\frac{5+\sqrt{17}}{2}\end{matrix}\right.\)