a: ĐKXĐ: \(x\ge1\)

b: ĐKXĐ: \(x< 0\)

c: ĐKXĐ: \(\left[{}\begin{matrix}x\ge11\\x\le3\end{matrix}\right.\)

1) ĐKXĐ: \(\left\{{}\begin{matrix}2x+11\ge0\\x-1\ge0\end{matrix}\right.\)\(\Leftrightarrow x\ge1\)

2) ĐKXĐ: \(\left\{{}\begin{matrix}-5x\ge0\\x\ne0\end{matrix}\right.\)\(\Leftrightarrow x< 0\)

3) ĐKXĐ: \(7x^2+1\ge0\left(đúng\forall x\right)\Leftrightarrow x\in R\)

4) ĐKXĐ: \(x^2-14x+33\ge0\Leftrightarrow\left(x-11\right)\left(x-3\right)\ge0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-11\ge0\\x-3\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x-11\le0\\x-3\le0\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x\ge11\\x\le3\end{matrix}\right.\)

5) ĐKXĐ: 

+) \(-x^2+6x+16\ge0\)

\(\Leftrightarrow-\left(x^2-6x+9\right)+25\ge0\)

\(\Leftrightarrow\left(x-3\right)^2\le25\Leftrightarrow-5\le x-3\le5\)

\(\Leftrightarrow-2\le x\le8\)

+) \(3x^2\ne0\Leftrightarrow x\ne0\)

\(\Rightarrow\left\{{}\begin{matrix}-2\le x\le8\\x\ne0\end{matrix}\right.\)

a) Biểu thức xác định `<=> x^2-2x-1>0`

`<=>(x^2-2x+1)-2>0`

`<=>(x-1)^2-(\sqrt2)^2>0`

`<=>(x-1+\sqrt2)(x-1-\sqrt2)>0`

`<=>` \(\left[{}\begin{matrix}x< 1-\sqrt{2}\\x>1+\sqrt{2}\end{matrix}\right.\)

`D=(-∞; 1-\sqrt2) \cup (1+\sqrt2 ; +∞)`

b) Biểu thức xác định `<=> x-\sqrt(2x+1)>0`

`<=> x>\sqrt(2x+1)`

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\2x+1\ge0\\x^2>2x+1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ge-\dfrac{1}{2}\\\left[{}\begin{matrix}x< 1-\sqrt{2}\\x>1+\sqrt{2}\end{matrix}\right.\end{matrix}\right.\\ \Leftrightarrow x>1+\sqrt{2}\)

`D=(1+\sqrt2 ; +∞)`

x∈[0, ∞)

\(\left\{{}\begin{matrix}16-x^2\ge0\\2x+1>0\\x^2-8x+14\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-4\le x\le4\\x>-\dfrac{1}{2}\\\left[{}\begin{matrix}x\ge4+\sqrt{2}\\x\le4-\sqrt{2}\end{matrix}\right.\end{matrix}\right.\Leftrightarrow-\dfrac{1}{2}< x\le4-\sqrt{2}\)

xác định \(< =>\left\{{}\begin{matrix}\sqrt{16-x^2}\ge0\\\sqrt{2x+1}>0\\\sqrt{x^2-8x+14}\ge0\end{matrix}\right.\)

\(< =>\left\{{}\begin{matrix}-4\le x\le4\\x>-\dfrac{1}{2}\\\left[{}\begin{matrix}x\le4-\sqrt{2}\\x\ge4_{ }+\sqrt{2}\end{matrix}\right.\\\end{matrix}\right.\)\(< =>-\dfrac{1}{2}< x\le4-\sqrt{2}\)

ĐKXĐ: \(\left\{{}\begin{matrix}16-x^2\ge0\\2x+1>0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2\le16\\x>-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le-4\\x>-\dfrac{1}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge4\\x>-\dfrac{1}{2}\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow x\ge4\)

\(1,\\ a,ĐK:\left\{{}\begin{matrix}x\ge0\\x+5\ge0\end{matrix}\right.\Leftrightarrow x\ge0\\ b,Sửa:B=\left(\sqrt{3}-1\right)^2+\dfrac{24-2\sqrt{3}}{\sqrt{2}-1}\\ B=4-2\sqrt{3}+\dfrac{2\sqrt{3}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}\\ B=4-2\sqrt{3}+2\sqrt{3}=4\\ 3,\\ =\left[1-\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{1+\sqrt{x}}\right]\cdot\dfrac{\sqrt{x}-3+2-2\sqrt{x}}{\left(1-\sqrt{x}\right)\left(\sqrt{x}-3\right)}-2\\ =\left(1-\sqrt{x}\right)\cdot\dfrac{-\sqrt{x}-1}{\left(1-\sqrt{x}\right)\left(\sqrt{x}-3\right)}-2\\ =\dfrac{-\sqrt{x}-1}{\sqrt{x}-3}-2=\dfrac{-\sqrt{x}-1-2\sqrt{x}+6}{\sqrt{x}-3}=\dfrac{-3\sqrt{x}+5}{\sqrt{x}-3}\)

a) ĐKXĐ: \(\left[{}\begin{matrix}x\ge\dfrac{5}{2}\\x< -2\end{matrix}\right.\)

b) ĐKXĐ: \(-\sqrt{2}\le x\le\sqrt{2}\)

c) ĐKXĐ: \(x\ge1\)

ĐKXĐ: \(x\ge0;x\ne1\)

Ta có: \(A=\left(2+\dfrac{2x+\sqrt{x}}{2\sqrt{x}+1}\right)\left(2-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right)\)

\(A=\left(2+\dfrac{\sqrt{x}\left(2\sqrt{x}+1\right)}{2\sqrt{x}+1}\right)\left(2-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\right)\)

\(A=\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)=4-x\)

a) để biểu thức có nghĩa thì \(\dfrac{2x-8}{x^2+1}\ge0\) mà \(x^2+1>0\)

\(\Rightarrow2x-8\ge0\Rightarrow x\ge4\)

b)  để biểu thức có nghĩa thì \(\dfrac{-x^2-3}{8x+10}\ge0\) mà \(-x^2-3=-\left(x^2+3\right)< 0\)

\(\Rightarrow8x+10< 0\Rightarrow x< -\dfrac{5}{4}\)

c)  để biểu thức có nghĩa thì \(x^2-2x+1>0\Rightarrow\left(x-1\right)^2>0\Rightarrow x\ne1\)

a) ĐKXĐ: \(x\ge4\)

b) ĐKXĐ: \(x< -\dfrac{5}{4}\)

c) ĐKXĐ: \(x\ne1\)