Ta có: \(\overline{87ab}\) chia hết cho 9
\(\Rightarrow8+7+a+b⋮9\)
\(\Rightarrow15+a+b⋮9\)
\(\Rightarrow a,b\in\left\{3,12\right\}\)
Lại có: \(a-b=4\)
. Nếu \(a+b=3;a-b=4\Rightarrow a=\left(3+4\right):2=3,5\) ( loại )
. Nếu \(a+b=12;a-b=4\Rightarrow a=\left(12+4\right):2=8\Rightarrow b=4\) ( nhận )
\(\Rightarrow a=8;b=4.\)
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Ta có: \(\left\{{}\begin{matrix}a-b=4\Rightarrow a=4+b\\\overline{87ab}=8700+10a+b\end{matrix}\right.\)
\(\Leftrightarrow\overline{87ab}=8700+10\left(4+b\right)+b\)
\(=8700+40+11b=8730+9b+9+1+2b\)
Vì \(\left\{{}\begin{matrix}\overline{87ab}⋮9\\8730+9b+9⋮9\end{matrix}\right.\)
Suy ra \(1+2b⋮9\)
Mà Bội của 9 gồm \(\left\{9;18;27;36;45;54;.....\right\}\)
\(\Rightarrow b\in\left\{4;13;22;....\right\}\)
\(\Rightarrow a\in\left\{8;17;...\right\}\)
Vì a,b là 1 chữ số nên \(\left\{{}\begin{matrix}a=8\\b=4\end{matrix}\right.\)
Vậy a=8;b=4
