Răspuns:
181
Explicație pas cu pas:
[tex]\textrm{Pentru } x = 0 \textrm{ avem:}\\ \\ |y| < 10\\ \\ -10 < y < 10 \implies \textrm{19 solutii}\\ \\ x = 1 \\ \\ 1+|y| < 10\\ \\ |y| < 9 \\ \\ -9 < y < 9 \implies \textrm{17 solutii}\\ \\ x = 2 \\ \\ 2+|y| < 10\\ \\ |y| < 8 \\ \\ -8 < y < 8 \implies \textrm{15 solutii}[/tex]
[tex]x = 3 \\ \\ 3 + |y| < 10 \\ \\ |y| < 7\\ \\ -7 < y < 7 \implies \textrm{13 solutii}\\ \\ x = 4 \\ \\ 4 + |y| < 10 \\ \\ |y| < 6 \\ \\ -6 < y < 6\implies \textrm{11 solutii} \\ \\ x = 5 \\ \\ 5 + |y| < 10 \\ \\ |y| < 5 \\ \\ -5 < y < 5\implies \textrm{9 solutii} \\ \\ x = 6 \\ \\ 6 + |y| < 10\\ \\ |y| < 4 \\ \\ -4 < y < 4 \implies \textrm{7 solutii}[/tex]
[tex]x = 7 \\ \\ -3 < y < 3 \implies \textrm{5 solutii}\\ \\ x = 8 \\ \\ -2 < y < 2 \implies \textrm{3 solutii}\\ \\ x = 9 \\ \\ -1 < y < 1 \implies \textrm{1 solutie} \\ \\ x = 10 \\ \\ 0 < y < 0 \implies \textrm{0 solutii}[/tex]
[tex]\textrm{Pentru fiecare valoare x pozitiva si nenula avem}\\ \\\textrm{ si opusul lui x de luat in considerare}(\times 2)\\ \\ Total = 19 + 2(17 + 15 + 13 + 11 + 9 + 7 + 5 + 3 + 1) = 19 + 2\cdot \frac{9(1 + 17)}{2} = 19 + 9\cdot 18 = 19 + 162 = 181[/tex]
