Question

Tìm x , y , z , t thỏa mãn :

\(\overline{xy}=\overline{yz}+\overline{zt^2}\)

Answer 1

\(1\le\overline{zt}^2\le81\Leftrightarrow1\le\overline{zt}\le9\)\(\Rightarrow z=0\)

\(PT\Leftrightarrow10x+y=10y+\overline{t}^2\)

\(\Leftrightarrow10x-9y=\overline{t}^2\)

(*) t=1 \(\Rightarrow10x-9y=1\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)

(*) t=2 \(\Rightarrow10x-9y=4\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=4\end{matrix}\right.\)

(*) t=3\(\Rightarrow10x-9y=9\Leftrightarrow\left\{{}\begin{matrix}x=9\\y=9\end{matrix}\right.\)

(*) t=4 \(\Rightarrow10x-9y=16\Leftrightarrow\left\{{}\begin{matrix}x=7\\y=6\end{matrix}\right.\)

(*) t=5 .....