Question

Tìm x;y thỏa : 

\(\overline{2x7y2}⋮36\)

Answer 1

Vì ( 4 ; 9 ) = 1

=> Số chia hết cho cả 4 và 9 thì chia hết cho 36

Ta có :  \(\overline{2x7y2}⋮9\Leftrightarrow2+x+7+y+2⋮9\Leftrightarrow11+x+y⋮9\)

             \(\overline{2x7y2}⋮4\Leftrightarrow\overline{y2}⋮4\Leftrightarrow y\in\left\{1;3;5;7;9\right\}\)

\(\left(+\right)y=1\Rightarrow x=6\)

\(\left(+\right)y=3\Rightarrow x=4\)

\(\left(+\right)y=5\Rightarrow x=2\)

\(\left(+\right)y=7\Rightarrow x=0\)

\(\left(+\right)y=9\Rightarrow x=7\)

Vậy \(\left(x;y\right)\in\left\{\left(1;6\right);\left(3;4\right);\left(5;2\right);\left(7;0\right);\left(9;7\right)\right\}\)