Răspuns:
[tex]m_{a} (a, b) = \frac{a + b}{2}[/tex]
[tex]m_{a} (a, b) = 4 \frac{5}{12} = \frac{4 \times 12 + 5}{12} = \frac{53}{12}[/tex]
a) să presupunem (la fel pentru restul exercițiilor) că
[tex]a = 5\frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{16}{3} [/tex]
[tex]m_{a} (a, b) = \frac{a + b}{2} = \frac{53}{12} [/tex]
[tex] \frac{a + b}{2} = \frac{53}{12} \\ a + b = 2 \times \frac{53}{12} \\ a + b = \frac{53}{6} \\ \frac{16}{3} + b = \frac{53}{6} \\ b = \frac{53}{6} - \frac{16}{3} \\ b = \frac{53 - 16 \times 2}{6} \\ b = \frac{21}{6} = \frac{7}{2} [/tex]
b)
[tex]a = 3 \frac{3}{4} = \frac{15}{4} [/tex]
[tex]b = \frac{53}{6} - \frac{15}{4} \\ b = \frac{106 - 45}{12} \\ b = \frac{61}{12} [/tex]
c)
[tex]a = 2 \frac{7}{9} = \frac{25}{9} [/tex]
[tex]b = \frac{53}{6} - \frac{25}{9} \\ b = \frac{53 \times 3 - 25 \times 2}{18} \\ b = \frac{159 - 50}{18} \\ b = \frac{109}{18} [/tex]
