Răspuns:
[tex]\bf \green{a)~ ~\overline{7a5}\in \{705,735,765,795\}~}[/tex]
[tex]\bf \blue{b)~~\overline{98a}\in \{981,984,987\}~}[/tex]
[tex]\bf \purple{c)~~\overline{4a8a}\in \{4080,4383,4686,4989\}~}[/tex]
[tex]\bf\red{d)~~\overline{4a5a}\in \{4353,4656,4959\}~}[/tex]
Explicație pas cu pas:
Criteriul de divizibilitate cu 3: "Un număr de divide cu 3 dacă și numai dacă suma cifrelor numărului respectiv se divide cu 3"
a)
[tex]\bf \overline{7a5} ~ \vdots~ 3\Leftrightarrow \text {\bf daca suma cifrelor se divide cu 3 }[/tex]
[tex]\bf a - cifra[/tex]
[tex]\bf a \in \{0,1,2,3,4,5,6,7,8,9 \}[/tex]
[tex]\bf 7+a+5 =( 12+a) \in M_{3}\Rightarrow( 12+a) \in \{12, 15, 18, 21 \}[/tex]
[tex]\bf \Rightarrow a \in \{0, 3,6,9\}\Rightarrow\green{\boxed{\bf ~\overline{7a5}\in \{705,735,765,795\}~}}[/tex]
---------------------------------
b)
[tex]\bf 9 + 8+a =( 17+a) \in M_{3}\Rightarrow( 17+a) \in \{18, 21,24 \}[/tex]
[tex]\bf \Rightarrow a \in \{1,4,7\}\Rightarrow\blue{\boxed{\bf~\overline{98a}\in \{981,984,987\}~}}[/tex]
---------------------------------
c)
[tex]\bf 4 + a+8+a =( 12+2a) \in M_{3}\Rightarrow( 12+2a) \in \{12,15,18,21,24,27,30 \}[/tex]
[tex]\bf \Rightarrow a \in \{0,3,6,9\}\Rightarrow\purple{\boxed{\bf~\overline{4a8a}\in \{4080,4383,4686,4989\}~}}[/tex]
---------------------------------
d)
[tex]\bf 4+a+5+a =( 9+2a) \in M_{3}\Rightarrow( 9+2a) \in \{9,12,15,18,21,24,27 \}[/tex]
[tex]\bf \Rightarrow a \in \{3,6,9\}\Rightarrow\red{\boxed{\bf~\overline{4a5a}\in \{4353,4656,4959\}~}}[/tex]
==pav38==
