Răspuns:
10; 30
Explicație pas cu pas:
a, b cifre în baza zece
[tex]\overline {ab}, a ≠ 0[/tex]
[tex] \frac{9}{ {a}^{2} + {b}^{2}} \in \mathbb{N} \implies {a}^{2} + {b}^{2}\in \{1;3;9\} \\ [/tex]
[tex]{a}^{2} + {b}^{2} = 1 \\ {a}^{2} \leqslant 1, a \not = 0 \implies a = 1 \\ 1 + {b}^{2} = 1 \iff {b}^{2} = 0 \: \implies b = 0 \\ \red{\bf \overline {ab} = 10}[/tex]
[tex]{a}^{2} + {b}^{2} = 3 \\ {a}^{2} \leqslant 3, a \not = 0 \implies a = 1 \\ 1 + {b}^{2} = 3 \iff {b}^{2} = 2 \: \implies b\not \in \mathbb{N} \\ \implies nu \: \: exista \: \: a \: si \: \: b[/tex]
[tex]{a}^{2} + {b}^{2} = 9 \\ {a}^{2} \leqslant 9, a \not = 0 \implies a \in \{1;2;3\} \\a = 1 \iff 1 + {b}^{2} = 9 \iff {b}^{2} = 8 \implies b\not \in \mathbb{N} \\ a = 2 \iff 4 + {b}^{2} = 9 \iff {b}^{2} = 5 \implies b\not \in \mathbb{N} \\ a = 3 \iff 9 + {b}^{2} = 9 \iff {b}^{2} = 0 \implies b = 0 \\ \red{\bf \overline {ab} = 30}[/tex]
