Question

10. Determină numerele naturale x şi y, ştiind că: (2x + 1)(5y - 3) = 30​

Answer 1

$1 \times 30 = 30 \\ 2 \times 15 = 30 \\ 3 \times 10 = 30 \\ 30 \times 1 = 30 \\ 15 \times 2 = 30 \\ 10 \times 3 = 30 \\ \\ \\ \\(2x + 1)(5y - 3) = 30 \\ 2x + 1 = 1 \\ x _{1} = 0 \\ 5y - 3 = 30 \\ y _{1} = \frac{33}{5} \\ \\ \underline{aceasta \: \: combinatie \: \: nu \: \: e \: \: buna. }\\ \\ \\ (2x + 1)(5y - 3) = 30 \\ 2x + 1 = 2 \\ x _{2} = \frac{1}{2} \\ \\ \underline{aceasta \: \: combinatie \: \: nu \: \: e \: \: buna.} \\ \\ \\ (2x + 1)(5y - 3) = 30 \\ 2x + 1 = 3 \\ x _{3} = 1 \\ 5y - 3 = 10 \\ y _{3} = \frac{13}{5} \\ \\ \underline{aceasta \: \: combinatie \: \: nu \: \: e \: \: buna.} \\ \\ \\ (2x + 1)(5y - 3) = 30 \\ 2x + 1 = 30 \\ x _{4} = \frac{29}{2} \\ \\ \underline{aceasta \: \: combinatie \: \: nu \: \: e \: \: buna.} \\ \\ \\ (2x + 1)(5y - 3) = 30 \\ 2x + 1 = 15 \\ x _{5} = 7 \\ 5y - 3 = 2 \\ y _{5} = 1 \\ \\ \underline{aceasta \: \: combinatie \: \: e \: \: buna. }\\ \\ \\ (2x + 1)(5y - 3) = 30 \\ 2x + 1 = 10 \\ x _{6} = \frac{9}{2} \\ \\ \underline{aceasta \: \: combinatie \: \: nu \: \: e \: \: buna. }\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \boxed{(x \: \c{} \: y) = (7 \: \c{} \: 1)}$