a) a=8
b) a=6; b=4; c=2
c) a=3; b=1
\(\left(a\right)\overline{a3}-17=66\)
\(\overline{a3}=66+17=83\)
a = 8
\(\left(b\right)\overline{a42}+\overline{b5}+\overline{10c}=789\)
\(a\cdot100+40+2+b\cdot10+5+100+c=789\)
\(\overline{abc}+147=789\)
\(\overline{abc}=789-147=642\)
a = 6; b = 4; c = 2
\(\left(c\right)\overline{ab}+281=\overline{ab0}+2\)
\(281-2=\overline{ab0}-\overline{ab}\)
\(279=\overline{ab}\cdot9\)
\(\overline{ab}=\frac{279}{9}=31\)
a = 3; b = 1
\(\left(d\right)\overline{2ab2}=\overline{ab}\cdot11+1989\)
\(2002+\overline{ab0}=\overline{ab}\cdot11+1989\)
\(2002-1989=\overline{ab}\cdot11-\overline{ab0}\)
\(\overline{ab}=13\)
a = 1; b = 3
\(\left(e\right)\overline{ab}\cdot6=\overline{a0b}\)
\(\left(a\cdot10+b\right)\cdot6=a\cdot100+b\)
\(a\cdot60+b\cdot6=a\cdot100+b\)
\(b\cdot6-b=a\cdot100-a\cdot60\)
\(b\cdot5=a\cdot40\)
\(b=a\cdot8\)
Suy ra a = 1; b = 8