\(\left(3x-1\right)^3=25\left(3x-1\right)\\ \Leftrightarrow\left(3x-1\right)^2=25\\ \Leftrightarrow\left[{}\begin{matrix}3x-1=5\\3x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{4}{3}\end{matrix}\right.\\ \left(3x-14\right)^3=2^5\cdot5^2+200\\ \Leftrightarrow\left(3x-14\right)^3=1000=10^3\\ \Leftrightarrow3x-14=10\Leftrightarrow x=8\)

\(\left(3x-1\right)^3=25\left(3x-1\right)\)

\(\Rightarrow\left(3x-1\right)\left(9x^2-6x+1-25\right)=0\)

\(\Rightarrow\left(3x-1\right)\left(9x^2-6x-24\right)=0\)

\(\Rightarrow3\left(3x-1\right)\left(x-2\right)\left(3x+4\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=2\\x=-\dfrac{4}{3}\end{matrix}\right.\)

\(\left(3x-14\right)^3=2^5.5^2+200\)

\(\Rightarrow\left(3x-14\right)^3=1000\)

\(\Rightarrow3x-14=10\Rightarrow3x=24\Rightarrow x=8\)

a) 2

b) 8

B

1: \(\left(3x-\dfrac{1}{5}\right)^2=\left(-\dfrac{3}{25}\right)^2\)

=>3x-1/5=3/25 hoặc 3x-1/5=-3/25

=>3x=8/25 hoặc 3x=2/25

=>x=8/75 hoặc x=2/75

2: \(\left(2x-\dfrac{1}{3}\right)^2=\left(-\dfrac{2}{9}\right)^2\)

=>2x-1/3=2/9 hoặc 2x-1/3=-2/9

=>2x=5/9 hoặc 2x=1/9

=>x=5/18 hoặc x=1/18

a) \(\left(3x-5\right)\left(9x^2+15x+25\right)\)

\(=\left(3x\right)^3-5^3\)

\(=27x^3-125\)

b) \(\left(2x+7\right)\left(x^2-14x+49\right)-2x\left(2x-1\right)\left(2x+1\right)\)

\(=2x^3-28x^2+98x+7x^2-98x+343-2x\left(4x^2-1\right)\)

\(=2x^3-28x^2+7x^2+343-8x^3+2x\)

\(=-6x^3-21x^2+343+2x\)

c) \(\left(4x-7\right)\left(16x^2+28x+49\right)\left(3x+1\right)\left(9x^2-3x+1\right)-9x\left(3x^2-1\right)\)

\(=\left(64x^3-343\right)\left(3x+1\right)\left(9x^2-3x+1\right)-27x^3+9x\)

\(=\left(6x^3-343\right)\left(27x^3+1\right)-27x^3+9x\)

\(=1728x^6+64x^3-9261x^3-343-27x^3+9x\)

\(=1728x^6-9224x^3-343+9x\)

Lời giải:
a)

\((4x-1)^2+(3x+1)^2+2(4x-1)(3x+1)\)

\(=(4x-1)^2+2(4x-1)(3x+1)+(3x+1)^2\)

\(=[(4x-1)+(3x+1)]^2=(7x)^2=49x^2\)

b)

\((x^2+2)(x-5)+(x-5)(x^2+5x+25)\)

\(=(x-5)[(x^2+2)+(x^2+5x+25)]\)

\(=(x-5)(2x^2+5x+27)\)

\(=\dfrac{3\left(x+1\right)\left(3x-5\right)}{-\left(3x-5\right)\left(3x+5\right)}=\dfrac{-3\left(x+1\right)}{3x+5}\)

\(=5\cdot\left(\dfrac{2}{5}-\dfrac{13}{12}\right):\left[-8\cdot\dfrac{11}{8}\right]\)

\(=5\cdot\dfrac{-41}{60}\cdot\dfrac{-1}{11}=\dfrac{205}{60\cdot11}=\dfrac{41}{132}\)

= 5. (0,4 - 13/12) : -11

= 5. -41/60 : -11

=-41/132

1:

\(\Leftrightarrow\sqrt{x-3}\left(\sqrt{x+3}-2\right)=0\)

=>x-3=0 hoặc \(\sqrt{x+3}=2\)

=>x=3 hoặc x+3=4

=>x=1(loại) hoặc x=3(nhận)

2:

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

=>\(4x-1+3x-4-2\sqrt{\left(4x+1\right)\left(3x-4\right)}=1\)

=>\(\sqrt{4\left(4x+1\right)\left(3x-4\right)}=7x-6\)

=>4(12x^2-16x+3x-4)=(7x-6)^2

=>49x^2-84x+36=48x^2-52x-16

=>-84x+36=-52x-16

=>-32x=-52

=>x=13/8

3: =>\(\sqrt{\left(x-5\right)^2}=5-x\)

=>|x-5|=5-x

=>x-5<=0

=>x<=5

4: \(\Leftrightarrow\left|x-4\right|=x+2\)

=>\(\left\{{}\begin{matrix}x>=-2\\\left(x-4\right)^2=\left(x+2\right)^2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-2\\x^2-8x+16=x^2+4x+4\end{matrix}\right.\)

=>x>=-2 và -8x+16=4x+4

=>x=1