Състезание

[Цанкова]

Задача 2

[Nathi123]

Нека [tex]A = [ab + 1 - ab(b+1) +a^{2}(b^{2}-1)+b](b-1) ; a =\frac{1}{1-b} ;[/tex]
[tex]A=[ab+1-ab^{2}-ab+a^{2}(b^{2} - 1) +b ](1-b) = [1 + b -\frac{b^{2}}{1-b} + \frac{b^{2}-1}{(1 -b)^{2}}](b-1) ,[/tex]защото[tex]a = \frac{1}{1 - b}[/tex]
[tex]\Rightarrow A = \frac{1-b^{2} - b^{2}-b-1 }{1-b}.(b-1) = 2b^{2}+b[/tex].