Răspuns:
[tex]\frac{2}{3}<\frac{3}{a}<\frac{7}{5}<\frac{3}{b}<\frac{6a}{2a+3b}[/tex]
a+b=?
a, b ∈ N*
[tex]\frac{2}{3}<\frac{3}{a}[/tex] ⇒ 2a<9 ⇒ [tex]a<\frac{9}{2}[/tex]
[tex]\frac{3}{a}<\frac{7}{5}[/tex] ⇒ 7a>15 ⇒ [tex]a>\frac{15}{7}[/tex]
[tex]\frac{15}{7}<a<\frac{9}{2}[/tex] ⇒ a∈{3, 4}
[tex]\frac{7}{5}<\frac{3}{b}[/tex] ⇒ 7b<15 ⇒ [tex]b<\frac{15}{7}[/tex] ⇒ b∈{1, 2}
daca b=1, a=3
[tex]\frac{2}{3}<\frac{3}{3}<\frac{7}{5}<\frac{3}{1}<\frac{6*3}{2*3+3*1}=\frac{18}{9}=2[/tex] FALS
daca b=1, a=4
[tex]\frac{2}{3}<\frac{3}{4}<\frac{7}{5}<\frac{3}{1}<\frac{6*4}{2*4+3*1}=\frac{24}{11}=2\frac{2}{11}[/tex] FALS
daca b=2, a=3
[tex]\frac{2}{3}<\frac{3}{3}<\frac{7}{5}<\frac{3}{2}<\frac{6*3}{2*3+3*2}=\frac{18}{12}=\frac{3}{2}[/tex] FALS
daca b=2, a=4
[tex]\frac{2}{3}<\frac{3}{4}<\frac{7}{5}<\frac{3}{2}<\frac{6*4}{2*4+3*2}=\frac{24}{14}=1\frac{10}{14}[/tex] ADEVARAT
a+b=4+2=3
Explicație pas cu pas:
