Explicație pas cu pas:
[tex]{(a + b)}^{2} = {( \sqrt{2 - \sqrt{2} } + \sqrt{2 + \sqrt{2} } )}^{2} = 2 - \sqrt{2} + 2 \sqrt{(2 - \sqrt{2} )(2 + \sqrt{2} )} + 2 + \sqrt{2} = 4 + 2 \sqrt{4 - 2} = \bf 4 + 2 \sqrt{2} [/tex]
[tex]\frac{b}{a} - \sqrt{2} = \frac{ \sqrt{2 + \sqrt{2} } }{ \sqrt{2 - \sqrt{2} } } - \sqrt{2} = \frac{ {( \sqrt{2 + \sqrt{2} } )}^{2} }{ \sqrt{2 - \sqrt{2} } \cdot \sqrt{2 + \sqrt{2} } } - \sqrt{2} = \frac{2 + \sqrt{2} }{ \sqrt{4 - 2} } - \sqrt{2} = \frac{2 + \sqrt{2} }{ \sqrt{2} } - \sqrt{2} = \frac{(2 + \sqrt{2}) \sqrt{2} }{2} - \sqrt{2} = \frac{2( \sqrt{2} + 1)}{2} - \sqrt{2} = \sqrt{2} + 1 - \sqrt{2} = \bf 1[/tex]
