Gọi 2 số lẻ liên tiếp là : \(2k+1;2k+3\left(k\in N\right)\)
Theo bài ra ta có :
\(\left(2k+3\right)^3-\left(2k+1\right)^3=6938\)
\(\Leftrightarrow\left(2k+3-2k-1\right)\left[\left(2k+3\right)^2+\left(2k+3\right)\left(2k+1\right)+\left(2k+1\right)^2\right]=6938\)
\(\Leftrightarrow2\left(4k^2+12k+9+4k^2+8k+3+4k^2+4k+1\right)=6938\)
\(\Leftrightarrow2\left(12k^2+24k+13\right)=6938\)
\(\Leftrightarrow12k^2+24k+13=3469\)
\(\Leftrightarrow12\left(k^2+2k+1\right)+1=3469\)
\(\Leftrightarrow12\left(k+1\right)^2=3468\)
\(\Leftrightarrow\left(k+1\right)^2=289\)
\(\Leftrightarrow\left[{}\begin{matrix}k+1=17\\k+1=-17\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}k=16\\k=-18\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2k+1=33\\2k+3=35\end{matrix}\right.\)
Vậy 2 số lẻ liên tiếp là : \(33;35\)
các bạn ới giúp mk ik mai mk hk r mk cần gấp lắm
