a, dk \(1-16x^2\ge0\Leftrightarrow\left(1-4x\right)\left(1+4x\right)\ge0\)

        \(\Leftrightarrow-\frac{1}{4}\le x\le\frac{1}{4}\)

b tuong tu

c, \(\sqrt{\left(x-3\right)\left(5-x\right)}\ge0\Leftrightarrow\left(x-3\right)\left(5-x\right)\ge0\Leftrightarrow3\le x\le5\)

d.\(\sqrt{x^2-x+1}>0\)

ma \(x^2-x+1=x^2-2.\frac{1}{2}x+\frac{1}{4}+\frac{3}{4}=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}>0\)

suy ra thoa man vs moi x

a/ \(1-16x^2\ge0\Rightarrow x^2\le16\Rightarrow-\frac{1}{4}\le x\le\frac{1}{4}\)

b/ \(\left\{{}\begin{matrix}x^2-3\ge0\\x^2-3\ne1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x\ge\sqrt{3}\\x\le-\sqrt{3}\end{matrix}\right.\\x\ne\pm2\end{matrix}\right.\)

c/ \(8x-x^2-15\ge0\Rightarrow3\le x\le5\)

d/ Hàm số xác định với mọi x

e/ \(\left\{{}\begin{matrix}x\ge\frac{1}{2}\\x\ne1\end{matrix}\right.\)

f/ \(\left\{{}\begin{matrix}-4\le x\le4\\x>-\frac{1}{2}\\\left[{}\begin{matrix}x\ge4+\sqrt{2}\\x\le4-\sqrt{2}\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow-\frac{1}{2}< x\le4-\sqrt{2}\)

a: \(A=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}}\)

\(=\sqrt{a}-\sqrt{b}-\sqrt{a}-\sqrt{b}=-2\sqrt{b}\)

b: \(B=\dfrac{2\sqrt{x}-x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{x+\sqrt{x}+1}{x-1}\)

\(=\dfrac{-2x+\sqrt{x}-1}{\sqrt{x}-1}\cdot\dfrac{1}{x-1}\)

c: \(C=\dfrac{x-9-x+3\sqrt{x}}{x-9}:\left(\dfrac{3-\sqrt{x}}{\sqrt{x}-2}+\dfrac{\sqrt{x}-2}{\sqrt{x}+3}+\dfrac{x-9}{x+\sqrt{x}-6}\right)\)

\(=\dfrac{3\left(\sqrt{x}-3\right)}{x-9}:\dfrac{9-x+x-4\sqrt{x}+4+x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{3}{\sqrt{x}+3}\cdot\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}{x-4\sqrt{x}+4}\)

\(=\dfrac{3}{\sqrt{x}-2}\)

\(a,\)\(\sqrt{\frac{1}{\left(x-3\right)^2}}\)

\(đk:\)\(\frac{1}{\left(x-3\right)^3}\ne0\)\(\Rightarrow\left(x-3\right)^3\ne0\)\(\Leftrightarrow x\ne3\)

Và \(\frac{1}{\left(x-3\right)}>0\Rightarrow x-3>0\)\(\Rightarrow x>3\)

Vậy để căn thức xác định thì x > 3

\(\sqrt{8x-x^2-15}\)

\(=\sqrt{-\left(x^2-8x+15\right)}\)

\(=\sqrt{-\left(x^2-8x+16-1\right)}\)

\(=\sqrt{-\left[\left(x^2-8x+16\right)-1\right]}\)

\(=\sqrt{-\left(x-4\right)^2+1}\)

\(đk:\)\(-\left(x-4\right)^2+1\ge0\)

\(\Rightarrow\left(x-4\right)^2\le1\)

\(\Rightarrow\orbr{\begin{cases}\left(x-4\right)^2=1\\\left(x-4\right)^2=0\end{cases}}\)

\(\left(x-4\right)^2=1\Rightarrow\orbr{\begin{cases}x=5\\x=3\end{cases}}\)

\(\left(x-4\right)^2=0\Rightarrow x=4\)

Vậy căn thức xác định \(\Leftrightarrow x=\left\{3;4;5\right\}\)

mình giúp bài 3 cho 

\(\sqrt{25x-125}-3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9x-45}=6\left(ĐKXĐ:x\ge5\right)\)

\(< =>\sqrt{25\left(x-5\right)}-3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9\left(x-5\right)}=6\)

\(< =>\sqrt{25}.\sqrt{x-5}-3\frac{\sqrt{x-5}}{\sqrt{9}}-\frac{1}{3}\sqrt{9}.\sqrt{x-5}=6\)

\(< =>5.\sqrt{x-5}-3.\frac{\sqrt{x-5}}{3}-\frac{1}{3}.3.\sqrt{x-5}=6\)

\(< =>5.\sqrt{x-5}-\sqrt{x-5}-\sqrt{x-5}=6\)

\(< =>3\sqrt{x-5}=6< =>\sqrt{x-5}=2\)

\(< =>x-5=4< =>x=4+5=9\left(tmđk\right)\)

Bài 1 :

a) \(ĐKXĐ:\hept{\begin{cases}x\ge0\\x\ne4\\x\ne9\end{cases}}\)

\(A=\left(1-\frac{\sqrt{x}}{\sqrt{x}+1}\right):\left(\frac{\sqrt{x}+3}{\sqrt{x}-2}+\frac{\sqrt{x}+2}{3-\sqrt{x}}+\frac{\sqrt{x}+2}{x-5\sqrt{x}+6}\right)\)

\(\Leftrightarrow A=\frac{\sqrt{x}+1-\sqrt{x}}{\sqrt{x}+1}:\frac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(\Leftrightarrow A=\frac{1}{\sqrt{x}+1}:\frac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)

\(\Leftrightarrow A=\frac{1}{\sqrt{x}+1}:\frac{1}{\sqrt{x}-2}\)

\(\Leftrightarrow A=\frac{\sqrt{x}-2}{\sqrt{x}+1}\)

b) Để \(A< -1\)

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

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

\(\Leftrightarrow2\sqrt{x}< 1\)

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

\(\Leftrightarrow x< \frac{1}{4}\)

Vậy để \(A< -1\Leftrightarrow x< \frac{1}{4}\)

Bài 1:

a, \(4\sqrt{3+2\sqrt{2}}-\sqrt{57+40\sqrt{2}}\)

\(=4\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{\left(4\sqrt{2}+5\right)^2}\)

\(=4\left(\sqrt{2}+1\right)-4\sqrt{2}-5\)

\(=4\sqrt{2}+4-4\sqrt{2}-5=-1\)

b, \(B=\sqrt{1100}-7\sqrt{44}+2\sqrt{176}-\sqrt{1331}\)

\(=10\sqrt{11}-14\sqrt{11}+8\sqrt{11}-11\sqrt{11}=-7\sqrt{11}\)

c, \(C=\sqrt{\left(1-\sqrt{2002}\right)^2}.\sqrt{2003+2\sqrt{2002}}\)

\(=\left(1-\sqrt{2002}\right).\sqrt{\left(\sqrt{2002}+1\right)^2}\)

\(=\left(1-\sqrt{2002}\right).\left(\sqrt{2002}+1\right)=-2001\)

Câu d bạn kiểm tra lại đề bài nhé.

Bài 2:

\(A=\frac{1}{2\sqrt{x}-2}-\frac{1}{2\sqrt{2}+2}+\frac{\sqrt{x}}{1-x}\)

a, ĐK: \(x\ge0,x\ne1\)

b, ĐK: \(x\ge0,x\ne1\)

 \(A=\frac{1}{2\sqrt{x}-2}-\frac{1}{2\sqrt{2}+2}+\frac{\sqrt{x}}{1-x}\)

\(=\frac{1}{2\sqrt{x}-2}-\frac{1}{2\sqrt{2}+2}-\frac{\sqrt{x}}{x-1}\)

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

\(=\frac{2\sqrt{x}+2-2\sqrt{x}+2}{4\left(x-1\right)}-\frac{\sqrt{x}}{x-1}\)

\(=\frac{4-4\sqrt{x}}{4\left(x-1\right)}=\frac{4\left(1-\sqrt{x}\right)}{4\left(1-x\right)}=\frac{1-\sqrt{x}}{1-x}\)

Thay \(x=3\left(TM\right)\)vào A ta có: \(A=\frac{1-\sqrt{3}}{3-1}=\frac{1-\sqrt{3}}{2}\)

Vậy với \(x=3\)thì \(A=\frac{1-\sqrt{3}}{2}\)

c, \(\left|A\right|=\frac{1}{2}\Leftrightarrow\orbr{\begin{cases}A=\frac{1}{2}\\A=-\frac{1}{2}\end{cases}}\)

TH1: \(A=\frac{1}{2}\)\(\Leftrightarrow\frac{1-\sqrt{x}}{x-1}=\frac{1}{2}\Leftrightarrow2-2\sqrt{x}=x-1\)\(\Leftrightarrow x-1-2+2\sqrt{x}=0\)\(\Leftrightarrow x+2\sqrt{x}-3=0\Leftrightarrow\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)=0\)\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x}-1=0\\\sqrt{x}+3=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\left(TM\right)\\\sqrt{x}=-3\left(L\right)\end{cases}}}\)

TH2: \(A=-\frac{1}{2}\Leftrightarrow\frac{1-\sqrt{x}}{x-1}=-\frac{1}{2}\)\(\Leftrightarrow2-2\sqrt{x}=1-x\Leftrightarrow-x+1-2+2\sqrt{x}=0\)\(\Leftrightarrow-x-1+2\sqrt{x}=0\Leftrightarrow x-2\sqrt{x}+1=0\)\(\Leftrightarrow\left(\sqrt{x}+1\right)^2=0\Leftrightarrow\sqrt{x}=-1\left(L\right)\)

Vậy với \(x=1\)thì \(\left|A\right|=\frac{1}{2}\)

Cám ơn bạn nhiều nha!!!