Explicație pas cu pas:
[tex]14a+15b=455[/tex]
[tex]14a = 5 \cdot (91 - 3b)[/tex]
[tex](5;14) = 1 \implies a \in \mathcal{M}_{5}[/tex]
[tex]14a < 455 \implies a \leqslant 30[/tex]
[tex]a \in \{5;10;15;20;25;30\}[/tex]
[tex]a = 5 \to 91 - 3b = 14 \to 3b = 77 \to b \not\in \mathbb{N}[/tex]
[tex]a = 10 \to 91 - 3b = 28 \to 3b = 63 \implies b = 21[/tex]
[tex]a = 15 \to 91 - 3b = 42 \to 3b = 49 \to b \not\in \mathbb{N}[/tex]
[tex]a = 20 \to 91 - 3b = 56 \to 3b = 35 \to b \not\in \mathbb{N}[/tex]
[tex]a = 25 \to 91 - 3b = 70 \to 3b = 21 \implies b = 7[/tex]
[tex]a = 30 \to 91 - 3b = 84 \to 3b = 7 \to b \not\in \mathbb{N}[/tex]
perechile de numere naturale (a,b) sunt: (10;21) și (25;7)
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Explicație pas cu pas:
[tex]14a+15b=455[/tex]
[tex]14a = 5 \cdot (91 - 3b)[/tex]
[tex](5;14) = 1 \implies a \in \mathcal{M}_{5}[/tex]
[tex]14a < 455 \implies a \leqslant 30[/tex]
[tex]a \in \{5;10;15;20;25;30\}[/tex]
[tex]a = 5 \to 91 - 3b = 14 \to 3b = 77 \to b \not\in \mathbb{N}[/tex]
[tex]a = 10 \to 91 - 3b = 28 \to 3b = 63 \implies b = 21[/tex]
[tex]a = 15 \to 91 - 3b = 42 \to 3b = 49 \to b \not\in \mathbb{N}[/tex]
[tex]a = 20 \to 91 - 3b = 56 \to 3b = 35 \to b \not\in \mathbb{N}[/tex]
[tex]a = 25 \to 91 - 3b = 70 \to 3b = 21 \implies b = 7[/tex]
[tex]a = 30 \to 91 - 3b = 84 \to 3b = 7 \to b \not\in \mathbb{N}[/tex]
perechile de numere naturale (a,b) sunt: (10;21) și (25;7)