Concursul "Teodor Topan" - problema 1

[maky]

Fie multimea \( A=\left{a\in\mathbb{Z}/\frac{\sqrt{7+4\sqrt3}-\sqrt{5-2\sqrt6}+\sqrt{11-6\sqrt2}} {2a-1}\in\mathbb{Z}\right} \).
Sa se verifice daca \( b=\frac{1}{\sqrt2+1}+\frac{1}{sqrt2-1}-\left(\sqrt2+1\right)^2+5 \) apartine multimii \( A \).

Crisan Georgeta, Simleu Silvaniei

[mihai++]

Expresia se transforma prin formare de patrate in:
\( E=\frac{11}{2a-1} \rightarrow a\in\left{-5,0,1,6} \).
Iar \( b=2 \not\in A \).