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a: ĐKXĐ: \(x\ge\dfrac{1}{3}\)
b: ĐKXĐ: \(x< \dfrac{15}{2}\)
c: ĐKXĐ: \(x\le0\)
a) \(\sqrt{x-2}+\dfrac{1}{x-5}\) có nghĩa khi:
\(\left\{{}\begin{matrix}x-2\ge0\\x-5\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x\ne5\end{matrix}\right.\)
b) \(\sqrt{\left(2x-6\right)\left(7-x\right)}=\sqrt{2\left(x-3\right)\left(7-x\right)}\) có nghĩa khi:
\(\left(x-3\right)\left(7-x\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3\ge0\\7-x\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x-3\le0\\7-x\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge3\\x\le7\end{matrix}\right.\\\left\{{}\begin{matrix}x\le3\\x\ge7\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow3\le x\le7\)
c) \(\sqrt{4x^2-25}=\sqrt{\left(2x-5\right)\left(2x+5\right)}\) có nghĩa khi:
\(\left(2x-5\right)\left(2x+5\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x-5\ge0\\2x+5\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}2x-5\le0\\2x+5\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge\dfrac{5}{2}\\x\ge-\dfrac{5}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x\le\dfrac{5}{2}\\x\le-\dfrac{5}{2}\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x\ge\dfrac{5}{2}\\x\le-\dfrac{5}{2}\end{matrix}\right.\)
d) \(\dfrac{2}{x^2-9}-\sqrt{5-2x}=\dfrac{2}{\left(x+3\right)\left(x-3\right)}-\sqrt{5-2x}\) có nghĩa khi:
\(\left\{{}\begin{matrix}x+3\ne0\\x-3\ne0\\5-2x\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\pm3\\x\le\dfrac{5}{2}\end{matrix}\right.\)
e) \(\dfrac{x}{x^2-4}+\sqrt{x-2}=\dfrac{x}{\left(x+2\right)\left(x-2\right)}+\sqrt{x-2}\) có nghĩa khi:
\(\left\{{}\begin{matrix}x-2\ne0\\x+2\ne0\\x-2\ge0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\pm2\\x\ge2\end{matrix}\right.\)
\(\Leftrightarrow x>2\)
\(1,\\ a,ĐK:11-2x\ge0\Leftrightarrow x\le\dfrac{11}{2}\\ b,ĐK:9x-18\ge0\Leftrightarrow x\ge2\\ c,ĐK:x\ne0;\dfrac{3}{x^2}\ge0\left(luôn.đúng.do.3>0;x^2>0\right)\Leftrightarrow x\in R\backslash\left\{0\right\}\\ d,ĐK:\dfrac{5}{x-7}\ge0\Leftrightarrow x-7>0\left(5>0;x-7\ne0\right)\Leftrightarrow x>7\\ 2,\\ a,=\left|4x\right|-2x^2=4x-2x^2\\ b,bạn.thiếu.điều.kiện.nhé\\ c,=\left|x-5\right|-4x=5-x-4x=5-5x\)
a) ĐKXĐ: \(x\in R\)
b) ĐKXĐ: \(-2\sqrt{2}+2\le x\le2\sqrt{2}+2\)
a) \(\sqrt{x^2-x+1}\)
\(=\sqrt{x^2-2\cdot\dfrac{1}{2}\cdot x+\dfrac{1}{4}+\dfrac{3}{4}}\)
\(=\sqrt{\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}}\)
Mà: \(\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}>0\forall x\)
Nên bt luôn có nghĩa
b) \(\dfrac{5}{\sqrt{1-\sqrt{x-1}}}\) có nghĩa khi:
\(\left\{{}\begin{matrix}x-1\ge0\\1-\sqrt{x-1}>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x-1< 1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}1\le x\\x< 2\end{matrix}\right.\Leftrightarrow1\le x< 2\)
c) \(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\) có nghĩa khi:
\(x\ge0\)
d) \(\dfrac{\sqrt{-3x}}{x^2-1}\) có nghĩa khi:
\(\Leftrightarrow\left\{{}\begin{matrix}-3x\ge0\\x^2-1\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\le0\\x\ne\pm1\end{matrix}\right.\)
e) \(\dfrac{2}{\sqrt{x}-2}\) có nghĩa khi:
\(\left\{{}\begin{matrix}x\ge0\\\sqrt{x}-2\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)
$a)ĐK:8x+2\ge 0$
$\to 8x \ge -2$
$\to x \ge -\dfrac14$
$b)ĐK:\dfrac{-5}{6-3x} \ge 0(x \ne 2)$
Mà $-5<0$
$\to 6-3x<0$
$\to 6<3x$
$\to x>2$
$*A=x-2\sqrt{x-2}+3(x \ge 2)$
$=x-2-2\sqrt{x-2}+1+4$
$=(\sqrt{x-2}-1)^2+4 \ge 4$
Dấu "=" xảy ra khi $\sqrt{x-2}-1=0 \Leftrightarrow \sqrt{x-2}=1\Leftrightarrow x=3$
a) ĐKXĐ: \(x\ge2\)
b) ĐKXĐ: \(\left[{}\begin{matrix}x\le1\\x\ge2\end{matrix}\right.\)
c) ĐKXĐ: \(\dfrac{x+3}{5-x}\ge0\)
\(\Leftrightarrow\dfrac{x+3}{x-5}\le0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+3\ge0\\x-5< 0\end{matrix}\right.\Leftrightarrow-3\le x< 5\)
a) Giá trị của x để biểu thức có nghĩa:
\(\sqrt{\frac{-5}{-x-7}}\ne0\Leftrightarrow\frac{-5}{-x-7}\ne0\Leftrightarrow-x-7\ne0\Leftrightarrow x\ne-7\)
b) Giá trị của x để biểu thức có nghĩa:
\(\sqrt{x^2+2x+3}\ne0\Leftrightarrow x^2+2x+1\ne-2\Leftrightarrow\left(x+1\right)^2\ne-2\Leftrightarrow x+1\ne-\sqrt{2}\Leftrightarrow x\ne-\sqrt{2}-1\)