\(\left(7x-11\right)^3=\left(-3\right)^2\cdot15+208\\ \Rightarrow\left(7x-11\right)^3=9\cdot15+208\\ \Rightarrow\left(7x-11\right)^3=135+208\\ \Rightarrow\left(7x-11\right)^3=343\\ \Rightarrow\left(7x-11\right)^3=7^3\\\Rightarrow7x-11=7\\ \Rightarrow7x=18\\ \Rightarrow x=\dfrac{18}{7} \)

( 7x - 11 )^3 = ( -3 ) ^2 x 15 + 208

( 7x - 11 )^3 =      9 x 15 + 208

( 7x - 11 )^3 =     135 + 208 

( 7x - 11 )^3 =          343 

( 7x - 11)^3  =      7^3 

7x - 11 = 7 

7x       = 18

  x       = 18/7

(7x-11)³=(-3)²x15+208

(7x-11)³=9x15+208

(7x-11)³=135+208

(7x-11)³=343

(7x-11)³=7³

7x-11=7

7x=7+11

7x=18

x=18 : 7

x=18/7

(7x-11)^3=9x15+208=135+208=343=7^3

7x-11=7

x=11+7:7

x=18/7

mình sửa lại nha, nãy mình nhìn nhầm dấu:

343x³ - 1617x² + 2541x - 1674 = 0

x = 18/7 là nghiệm duy nhất của phương trình đã cho

a)

 \(\left(2x-15\right)^5=\left(2x-15\right)^3\\ \Leftrightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\\ \Leftrightarrow\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15-1\right).\left(2d-15+1\right)=0\end{matrix}\right.\\\Leftrightarrow\left[{}\begin{matrix}2x-15=0\\2x-16=0\\2x-14=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=7\end{matrix}\right. \)

b) \(\left(7x-11\right)^3=\left(-3\right)^2.15+208\\ \Leftrightarrow\left(7x-11\right)^3=343=7^3\\ \Leftrightarrow7x-11=7\\ \Leftrightarrow x=\dfrac{18}{7}\)

( 7x - 11 ) ³ = ( -3 )² .15 + 208

( 7x - 11 ) ³ = 9 .15 + 208

( 7x - 11 ) ³ = 135 + 208

( 7x - 11 ) ³ = 343

( 7x - 11 ) ³ = 7³

=> 7x - 11 = 7

=> 7x = 7 + 11 = 18

=> x = 18/7

\(\left(7x-11\right)^3=\left(-3\right)^2.15+208\)

\(\Leftrightarrow\)\(\left(7x-11\right)^3=9.15+208\)

\(\Leftrightarrow\)\(\left(7x-11\right)^3=135+208\)

\(\Leftrightarrow\)\(\left(7x-11\right)^3=343\)

\(\Leftrightarrow\)\(\left(7x-11\right)^3=7^3\)

\(\Leftrightarrow\)\(7x-11=7\)

\(\Leftrightarrow\)\(7x=18\)

\(\Leftrightarrow\)\(x=\frac{18}{7}\)

Vậy \(x=\frac{18}{7}\)

Chúc bạn học tốt ~ 

bài này dễ mà

bai nay hay nhung de

1) \(x=\frac{8}{-3}-\frac{1}{2}=\frac{-19}{6}\)

2) \(\left(\frac{-5}{3}\right)^3=\frac{-125}{27}\)

     \(\frac{-24}{35}.\frac{-5}{6}=\frac{4}{7}\)

Mà \(\frac{-125}{27}<0<\frac{4}{7}\)

=> \(x=0\)

3) \(\left(7.x-11\right)^3=343\)

=> \(\left(7.x-11\right)^3=7^3\)

=> \(7.x-11=7\)

=> \(x=\frac{7+11}{7}=\frac{18}{7}\)

\(x\inℤ\) hả 

x thuộc Z

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