Lời giải:
\((7x-11)^3=2^5.5^2+200=1000\)
\(\Leftrightarrow (7x-11)^3=10^3\)
\(\Rightarrow 7x-11=10\Rightarrow x=\frac{11+10}{7}=3\)
Vậy $x=3$
\(\left(7x-11\right)^3=2^5\cdot5^2+200\)
\(\left(7x-11\right)^3=32\cdot25+200\)
\(\left(7x-11\right)^3=800+200\)
\(\left(7x-11\right)^3=1000\)
\(\left(7x-11\right)^3=10^3\)
\(\Rightarrow7x-11=10\)
\(7x=11+10\)
\(7x=21\)
\(x=21:7\)
\(x=3\)