Răspuns:
Explicație pas cu pas:
[tex]a<b !!!\\a)~a<\frac{2a+b}{3}<\frac{a+2b}{3}<b.~Tr~sa~dem~adevarul~a~3~inegalitati\\a<\frac{2a+b}{3}~|*3~3a<2a+b,~3a-2a<b,~a<b~Adevarat.\\\frac{2a+b}{3}<\frac{a+2b}{3},~|*3,~2a+b<a+2b,~2a-a<2b-b,~a<b,~Adevarat.\\\frac{a+2b}{3}<b,~|3,~a+2b<3b,~a<3b-2b,~a<b,~Adevarat!!!\\b)~a<\frac{3a+b}{4}<\frac{a+b}{2}<\frac{a+3b}{4}<b.\\Tr~sa~dem~adevarul~a~4~inegalitati\\a<\frac{3a+b}{4},~|*4,~4a<3a+b,~4a-3a<b,~a<b,~Adevarat.\\\frac{3a+b}{4}<\frac{a+b}{2},~|*4,~3a+b<2*(a+b),~3a+b<2a+2b,~a<b,~Adevarat\\[/tex]
[tex]\frac{a+b}{2}<\frac{a+3b}{4},~|*4,~2(a+b)<a+3b,~2a+2b<a+3b,~a<b,~Adevarat.\\\frac{a+3b}{4}<b,~|*4,~a+3b<4b,~a<4b-3b,~a<b,~Adevarat !!!![/tex]
