Răspuns:
[tex]d) \frac{0.2 + 0.(2) }{2x + 1} = \frac{1}{45} \\ (0.2 + 0.(2)) \times 45 = (2x + 1) \times 1 \\ (\frac{2}{10} + \frac{2}{9} ) \times 45 = 2x + 1 \\ ( \frac{2 \times 9}{90} + \frac{2 \times 10}{90} ) \times 45 = 2x + 1 \\ ( \frac{18}{90} + \frac{20}{90} ) \times 45 = 2x + 1 \\ \frac{38}{90} \times 45 = 2x + 1 \\ \frac{38}{2} \times 1 = 2x + 1 \\ 19 = 2x + 1 \\ 2x = 19 - 1 \\ 2x = 18 \\ x = 9[/tex]
[tex]e) \frac{ {2}^{51} - {2}^{50} - {2}^{49} }{ {8}^{16} } = \frac{ 31x}{992} \\ \frac{ {2}^{49} \times ( {2}^{2} - 2 - 1) }{( {2}^{3} ) ^{16} } = \frac{31x}{992} \\ \frac{ {2}^{49} \times (4 - 2 - 1)}{ {2}^{48} } = \frac{31x}{992} \\ \frac{ {2}^{49} \times 1 }{ {2}^{48} } = \frac{31x}{992} \\ \frac{2}{1} = \frac{31x}{992} \\ 31x = 992 \times 2 \\ 31x = 1984 \\ x = 1984 \div 31 = 64[/tex]
[tex]f) \frac{x}{14 + {2}^{2} } = \frac{8}{x} \\ \frac{x}{14 + 4} = \frac{8}{x} \\ \frac {x}{18} = \frac{8}{x} \\ x \times x = 18 \times 8 \\ {x}^{2} = 144 \\ {x}^{2} = {12}^{2} \\ x = 12[/tex]
