\(\left(x-2\right)\left(x^2+6x-11\right)^2=\left(5x^2-10x+1\right)^2\) \(\Rightarrow x>2\)

\(\Rightarrow x^2+6x-11>0\)

\(pt\Leftrightarrow x-2=\left(\dfrac{5x^2-10x+1}{x^2+6x-11}\right)^2\Leftrightarrow\sqrt{x-2}=\dfrac{5x^2-10x+1}{x^2+6x-11}\)

\(\Leftrightarrow\sqrt{x-2}-1=\dfrac{5x^2-10x+1}{x^2+6x-11}-1=\dfrac{4x^2-16x+12}{x^2+6x+12}\)

\(\Leftrightarrow\dfrac{x-3}{\sqrt{x-2}+1}=\dfrac{4\left(x-1\right)\left(x-3\right)}{x^2+6x-11}\)

\(\Rightarrow\left[{}\begin{matrix}x-3=0\Rightarrow x=3\\\dfrac{1}{\sqrt{x-2}+1}=\dfrac{4\left(x-1\right)}{x^2+6x-11}\left(1\right)\end{matrix}\right.\)

Xét (1):

\(x^2+6x-11=4\left(x-1\right)+4\left(x-1\right)\sqrt{x-2}\)

\(\Leftrightarrow x^2+2x-7-4\left(x-1\right)\sqrt{x-2}=0\)

\(\Leftrightarrow x^2-2x+1-2\left(x-1\right)\sqrt{4x-8}+4x-8=0\)

\(\Leftrightarrow\left(x-1\right)^2-2\left(x-1\right)\sqrt{4x-8}+\left(\sqrt{4x-8}\right)^2=0\)

\(\Leftrightarrow\left(x-1-\sqrt{4x-8}\right)^2=0\)

\(\Leftrightarrow x-1=\sqrt{4x-8}\)

\(\Leftrightarrow x^2-2x+1=4x-8\)

\(\Leftrightarrow\left(x-3\right)^2=0\Rightarrow x=3\)

Vậy pt đã cho có nghiệm duy nhất \(x=3\)

Đặt \(y=x-2\), phương trình đã cho trở thành:

\( y{\left[ {{{\left( {y + 2} \right)}^2} + 6\left( {y + 2} \right) - 11} \right]^2} = {\left[ {5{{\left( {y + 2} \right)}^2} - 10\left( {y + 2} \right) + 1} \right]^2}\\ \Leftrightarrow y{\left( {{y^2} + 10y + 5} \right)^2} = {\left( {5{y^2} + 10y + 1} \right)^2}\\ \Leftrightarrow {y^5} - 5{y^4} + 10{y^3} - 10{y^2} + 5y - 1 = 0 \Leftrightarrow {\left( {y - 1} \right)^5} = 0 \Leftrightarrow y = 1 \)

Với \(y=1\) ta có \(x-2=1\) \(\Rightarrow x=3\)

Vậy \(x = 3 \)

a) \(\left(3x+2\right)^2-\left(3x-2\right)^2=5x+8\)

\(\Rightarrow\left(3x+2+3x-2\right)\left(3x+2-3x+2\right)=5x+8\)

\(\Rightarrow4.6x=5x+8\Rightarrow24x=5x+8\)

\(\Rightarrow19x=8\Rightarrow x=\frac{8}{19}\)

b) \(3\left(x-2\right)^2+9\left(x-1\right)=3\left(x^2+x-3\right)\)

\(\Rightarrow3\left(x^2-4x+4\right)+9x-9=3x^2+3x-9\)

\(\Rightarrow3x^2-12x+12+9x-9=3x^2+3x-9\)

\(\Rightarrow-12x+12+9x-9=3x-9\)

\(\Rightarrow-3x+3=3x-9\)

\(\Rightarrow6x=12\Rightarrow x=2\)

c) \(\left(x+3\right)^2-\left(x-3\right)^2=6x+18\)

\(\Rightarrow\left(x+3+x-3\right)\left(x+3-x+3\right)=6x+18\)

\(\Rightarrow2x.6=6x+18\Rightarrow6x=18\Rightarrow x=3\)

a: =>(x^2+4x-5)(x^2+4x-21)=297

=>(x^2+4x)^2-26(x^2+4x)+105-297=0

=>x^2+4x=32 hoặc x^2+4x=-6(loại)

=>x^2+4x-32=0

=>(x+8)(x-4)=0

=>x=4 hoặc x=-8

b: =>(x^2-x-3)(x^2+x-4)=0

hay \(x\in\left\{\dfrac{1+\sqrt{13}}{2};\dfrac{1-\sqrt{13}}{2};\dfrac{-1+\sqrt{17}}{2};\dfrac{-1-\sqrt{17}}{2}\right\}\)

c: =>(x-1)(x+2)(x^2-6x-2)=0

hay \(x\in\left\{1;-2;3+\sqrt{11};3-\sqrt{11}\right\}\)

a: ĐKXĐ: \(4x-3>0\)

=>x>3/4

\(log_5\left(4x-3\right)=2\)

=>\(log_5\left(4x-3\right)=log_525\)

=>4x-3=25

=>4x=28

=>x=7(nhận)

b: ĐKXĐ: \(x\ne0\)

\(log_2x^2=2\)

=>\(log_2x^2=log_24\)

=>\(x^2=4\)

=>\(\left[{}\begin{matrix}x=2\left(nhận\right)\\x=-2\left(nhận\right)\end{matrix}\right.\)

c: ĐKXĐ: \(x\notin\left\{-\dfrac{1}{2};\dfrac{3}{2}\right\}\)

\(\log_52x+1=\log_5-2x+3\)

=>2x+1=-2x+3

=>4x=2

=>\(x=\dfrac{1}{2}\left(nhận\right)\)

d: ĐKXD: \(x\notin\left\{3\right\}\)

\(ln\left(x^2-6x+7\right)=ln\left(x-3\right)\)

=>\(x^2-6x+7=x-3\)

=>\(x^2-7x+10=0\)

=>(x-2)(x-5)=0

=>\(\left[{}\begin{matrix}x=2\left(nhận\right)\\x=5\left(nhận\right)\end{matrix}\right.\)

e: ĐKXĐ: \(x\notin\left\{\dfrac{1}{5};2\right\}\)

\(log\left(5x-1\right)=log\left(4-2x\right)\)

=>5x-1=4-2x

=>7x=5

=>\(x=\dfrac{5}{7}\left(nhận\right)\)