Question

Am nevoie de exercitiul 1a! Repede va rog din suflet ofer coroana!

Answer 1

Răspuns:

A = {1; 3; 4}

Explicație pas cu pas:

$\dfrac{\sqrt{7+4\sqrt 3}-2\sqrt{5-2\sqrt 6}-\sqrt{11-4\sqrt 6}}{x-2} = \\ \\ = \dfrac{\sqrt{(\sqrt 3 + 2)^2} - 2\sqrt{(\sqrt 3 - \sqrt 2)^2}-\sqrt{(2\sqrt 2 - \sqrt 3)^2}}{x-2} = \\ \\ = \dfrac{|\sqrt 3+2| - 2|\sqrt 3 - \sqrt 2| - |2\sqrt 2 - \sqrt 3|}{x-2} = \\ \\ = \dfrac{\sqrt 3 + 2 - 2(\sqrt 3 - \sqrt 2) - (2\sqrt 2 - \sqrt 3)}{x-2} = \\ \\ = \dfrac{\sqrt 3 -2\sqrt 3 + \sqrt 3 +2\sqrt 2 - 2\sqrt 2 +2}{x-2} = \\ \\ = \dfrac{2}{x-2} \in \mathbb{Z}$

$\Rightarrow x-2 \in D_{2} \Rightarrow x-2\in \{-2;-1;1;2\}\Big| +2\Rightarrow \\ \\ \Rightarrow x \in \{0;1;3;4\} \\ \\ \Rightarrow A = \{0;1;3;4\} \cap \mathbb{Z}^*\\ \\ \Rightarrow \boxed{A = \{1;3;4\}}$