a) \(\sqrt[]{x^2-4x+4}=x+3\)

\(\Leftrightarrow\sqrt[]{\left(x-2\right)^2}=x+3\)

\(\Leftrightarrow\left|x-2\right|=x+3\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=x+3\\x-2=-\left(x+3\right)\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}0x=5\left(loại\right)\\x-2=-x-3\end{matrix}\right.\)

\(\Leftrightarrow2x=-1\Leftrightarrow x=-\dfrac{1}{2}\)

b) \(2x^2-\sqrt[]{9x^2-6x+1}=5\)

\(\Leftrightarrow2x^2-\sqrt[]{\left(3x-1\right)^2}=5\)

\(\Leftrightarrow2x^2-\left|3x-1\right|=5\)

\(\Leftrightarrow\left|3x-1\right|=2x^2-5\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=2x^2-5\\3x-1=-2x^2+5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x^2-3x-4=0\left(1\right)\\2x^2+3x-6=0\left(2\right)\end{matrix}\right.\)

Giải pt (1)

\(\Delta=9+32=41>0\)

Pt \(\left(1\right)\) \(\Leftrightarrow x=\dfrac{3\pm\sqrt[]{41}}{4}\)

Giải pt (2)

\(\Delta=9+48=57>0\)

Pt \(\left(2\right)\) \(\Leftrightarrow x=\dfrac{-3\pm\sqrt[]{57}}{4}\)

Vậy nghiệm pt là \(\left[{}\begin{matrix}x=\dfrac{3\pm\sqrt[]{41}}{4}\\x=\dfrac{-3\pm\sqrt[]{57}}{4}\end{matrix}\right.\)

2: =>2x^2-8x+4=x^2-4x+4 và x>=2

=>x^2-4x=0 và x>=2

=>x=4

3: \(\sqrt{x^2+x-12}=8-x\)

=>x<=8 và x^2+x-12=x^2-16x+64

=>x<=8 và x-12=-16x+64

=>17x=76 và x<=8

=>x=76/17

4: \(\sqrt{x^2-3x-2}=\sqrt{x-3}\)

=>x^2-3x-2=x-3 và x>=3

=>x^2-4x+1=0 và x>=3

=>\(x=2+\sqrt{3}\)

6:

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

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

=>\(\left|\sqrt{x-1}-1\right|=\sqrt{x-1}+1+2=\sqrt{x-1}+3\)

=>1-căn x-1=căn x-1+3 hoặc căn x-1-1=căn x-1+3(loại)

=>-2*căn x-1=2

=>căn x-1=-1(loại)

=>PTVN

1) ĐK: \(x\ge\dfrac{5}{2}\)

pt <=> \(x-4=\sqrt{2x-5}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\\left(x-4\right)^2=2x-5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\x^2-8x+16=2x-5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\x^2-10x+21=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\\left(x-3\right)\left(x-7\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge4\\\left[{}\begin{matrix}x=3\left(l\right)\\x=7\left(n\right)\end{matrix}\right.\end{matrix}\right.\)

Vậy, pt có nghiệm duy nhất là x=7

2) ĐK: \(2x^2-8x+4\ge0\)

pt <=> \(\left\{{}\begin{matrix}x\ge2\\2x^2-8x+4=x^2-4x+4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x^2-4x=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x\left(x-4\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\\left[{}\begin{matrix}x=0\left(l\right)\\x=4\left(n\right)\end{matrix}\right.\end{matrix}\right.\)

Vậy, pt có nghiệm duy nhất là x=4

3) ĐK: \(x\ge3\)

pt <=> \(\left\{{}\begin{matrix}x\le8\\x^2+x-12=x^2-16x+64\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\le8\\17x=76\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\le8\\x=\dfrac{76}{17}\left(n\right)\end{matrix}\right.\) 

Vậy, pt có nghiệm duy nhất là \(x=\dfrac{76}{17}\)\(\)

4) ĐK: \(x\ge3\)

pt <=> \(x^2-3x-2=x-3\)

\(\Leftrightarrow x^2-4x+1=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2+\sqrt{3}\left(n\right)\\x=2-\sqrt{3}\left(l\right)\end{matrix}\right.\)

a) \(6\sqrt{x-1}-\dfrac{1}{3}\cdot\sqrt{9x-9}+\dfrac{7}{2}\sqrt{4x-4}=24\) (ĐK: \(x\ge1\)) 

\(\Leftrightarrow6\sqrt{x-1}-\dfrac{1}{3}\cdot\sqrt{9\left(x-1\right)}+\dfrac{7}{2}\sqrt{4\left(x-1\right)}=24\)

\(\Leftrightarrow6\sqrt{x-1}-\dfrac{1}{3}\cdot3\sqrt{x-1}+\dfrac{7}{2}\cdot2\sqrt{x-1}=24\)

\(\Leftrightarrow6\sqrt{x-1}-\sqrt{x-1}+7\sqrt{x-1}=24\)

\(\Leftrightarrow12\sqrt{x-1}=24\)

\(\Leftrightarrow\sqrt{x-1}=\dfrac{24}{12}\)

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

\(\Leftrightarrow x-1=4\)

\(\Leftrightarrow x=4+1\)

\(\Leftrightarrow x=5\left(tm\right)\)

b) \(\dfrac{1}{2}\sqrt{4x+8}-2\sqrt{x+2}-\dfrac{3}{7}\sqrt{49x+98}=-8\) (ĐK: \(x\ge-2\))

\(\Leftrightarrow\dfrac{1}{2}\cdot2\sqrt{x+2}-2\sqrt{x+2}-\dfrac{3}{7}\cdot7\sqrt{x+2}=-8\)

\(\Leftrightarrow\sqrt{x+2}-2\sqrt{x+2}-3\sqrt{x+2}=-8\)

\(\Leftrightarrow-4\sqrt{x+2}=-8\)

\(\Leftrightarrow\sqrt{x+2}=\dfrac{-8}{-4}\)

\(\Leftrightarrow\sqrt{x+2}=2\)

\(\Leftrightarrow x+2=4\)

\(\Leftrightarrow x=4-2\)

\(\Leftrightarrow x=2\left(tm\right)\)

a) căn(2x+5) - căn(3-x) = x² -5x + 8 
Điều kiện : \(-\frac{5}{2}\Leftarrow x\Leftarrow3\)
căn(2x+5) - căn(3-x) = x^2-5x+8 
\(\Leftrightarrow\)[căn(2x+5)-3]-[căn(3-x)-1]=x² -5x+6 
nhân liên hợp 
\(\Leftrightarrow\)(2x+5-9) / [căn(2x+5)+3] -(3-x-1) / [căn (3-x)+1]=(x-2)(x-3) 
\(\Leftrightarrow\)(2x-4) / [căn (2x+5)+3] -(2-x) /  [ căn (3-x)+1]-(x-2)(x-3)=0 
\(\Leftrightarrow\)(x-2).M=0 
\(\Leftrightarrow\)x=2 hoặc M=0 
M=2 / [căn(2x+5)+3]+1 / [căn(3-x)+1]-x+3 

2/[can(2x+5)+3]+1/[can(3-x)+1]>0 voi moi x 
voi -5/2<=x<=3 <->3-x thuoc[0;11/2] 
nen M>0 
vay x=2 
b/ 2+ căn(3-8x) = 6x + căn(4x-1) 
dk[1/4;8/3] 
6x-2+căn(4x-1)-căn(3-8x)=0 
<->2(3x-1)+(4x-1-3+8x)/[căn(4x-1)+căn(... 
<->2(3x-1)+(12x-4)/[căn(4x-1)+căn(3-8x... 
<->2(3x-1)+4(3x-1)/[căn(4x-1)+căn(3-8x... 
<->(3x-1){2+4/[căn(4x-1)+căn(3-8x)]}=0 
2+4/[căn(4x-1)+căn(3-8x)>0 
nen 3x-1=0 
x=1/3

 a)  căn(2x+5) - căn(3-x) = x^2-5x+8 
dkxd -5/2<=x<=3 
căn(2x+5) - căn(3-x) = x^2-5x+8 
<->[can(2x+5)-3]-[can(3-x)-1]=x^2-5x+6 
nhan lien hop 
<->(2x+5-9)/[can(2x+5)+3] -(3-x-1)/[can(3-x)+1]=(x-2)(x-3) 
<->(2x-4)/[can(2x+5)+3] -(2-x)/[can(3-x)+1]-(x-2)(x-3)=0 
<->(x-2).M=0 
<->x=2 hoac M=0 
M=2/[can(2x+5)+3]+1/[can(3-x)+1]-x+3 

2/[can(2x+5)+3]+1/[can(3-x)+1]>0 voi moi x 
voi -5/2<=x<=3 <->3-x thuoc[0;11/2] 
nen M>0 
vay x=2 
b/ 2+ căn(3-8x) = 6x + căn(4x-1) 
dk[1/4;8/3] 
6x-2+căn(4x-1)-căn(3-8x)=0 
<->2(3x-1)+(4x-1-3+8x)/[căn(4x-1)+căn(... 
<->2(3x-1)+(12x-4)/[căn(4x-1)+căn(3-8x... 
<->2(3x-1)+4(3x-1)/[căn(4x-1)+căn(3-8x... 
<->(3x-1){2+4/[căn(4x-1)+căn(3-8x)]}=0 
2+4/[căn(4x-1)+căn(3-8x)>0 
nen 3x-1=0 
x=1/3