Răspuns:
[tex]{( \sqrt{2} - \sqrt{6} - 1) }^{2} = {[( \sqrt{2} - \sqrt{6}] - 1) }^{2} = \\ [/tex]
Folosim formula (a - b)² = a² - 2ab + b²
[tex]= (\sqrt{2} - \sqrt{6})^2 - 2 \cdot (\sqrt{2} - \sqrt{6}) \cdot 1 + 1 \\ [/tex]
[tex]= (\sqrt{2})^2 - 2 \sqrt{2} \cdot \sqrt{6}^2 + (\sqrt{6})^2 - 2\sqrt{2} + 2\sqrt{6} + 1 \\ [/tex]
[tex]= 2 - 2 \sqrt{ {2}^{2} \cdot 3 } + 6 - 2\sqrt{2} + 2\sqrt{6} + 1 \\ [/tex]
[tex]= 2 - 4 \sqrt{3} + 6 - 2\sqrt{2} + 2\sqrt{6} + 1 \\ [/tex]
[tex]= \bf 9 + 2\sqrt{6} - 4 \sqrt{3} - 2\sqrt{2}[/tex]
Sau folosim formula:
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
