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

(7x - 11)³ = 2⁵ * 2² + 200

= (7x - 11)³ = 128 + 200

= 7x - 11³ = 328

= 7x - 1331 = 328

= 7x = 328 + 1331

= 7x = 1659

= x = 1659 : 7 

= x = 237

Vậy x = 237

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

\(\left(7x-11\right)^3=2^5.5^2+200\)

=> \(\left(7x-11\right)^3=32.25+200\)

=>\(\left(7x-11\right)^3=800+200\)

=>\(\left(7x-11\right)^3=1000\)

=>\(\left(7x-11\right)^3=10^3\)

=> \(7x-11=10\)

=>\(7x=21\)

=>\(x=3\)

Vậy x = 3

\(\left(7x-11\right)^3=2^5\cdot5^2+200\)

\(\left(7x-11\right)^3=800+200\)

\(\left(7x-11\right)^3=1000\)

\(\left(7x-11\right)^3=10^3\)

\(\Rightarrow7x-11=10\)

\(7x=10+11\)

\(7x=21\)

\(x=21\div7\)

\(x=3\)

\(\left(7x-11\right)^3=2^5\cdot5^2+200\)

\(\left(7x-11\right)^3=32\cdot25+200\)

\(\left(7x-11\right)^3=1000\)

\(\left(7x-11\right)^3=10^3\)

\(7x-11=10\)

\(7x=21\)

\(x=3\)

(7x-11)³=(-3)³.15+208

(7x-11)³=-27.15+208

(7x-11)³=-405+208

(7x-11)³=-197

Vô lí vì -197 ko chuyển sang mũ 3 đc.

Vậy \(x\in\varnothing\)

Tao ghét mây đứa tên trâm