[tex]x = \frac{1}{ \sqrt{2} - 1 } + \frac{1}{ \sqrt{2} + 1} = \frac{ \sqrt{2} + 1 + ( \sqrt{2 } - 1)}{( \sqrt{2} + 1)( \sqrt{2} - 1) } [/tex]
[tex]x = \frac{ \sqrt{2} + 1 + \sqrt{2} - 1 }{ { \sqrt{2} }^{2} - 1} = \frac{2 \sqrt{2} }{2 - 1} = 2 \sqrt{2} [/tex]
[tex]y = \sqrt{2} \times ( \sqrt{2} + \frac{1}{ \sqrt{2} } )[/tex]
[tex]y = \sqrt{2} \times ( \frac{ \sqrt{2} \times \sqrt{2} + 1}{ \sqrt{2} } )[/tex]
[tex]y = \sqrt{2} \times \frac{3}{ \sqrt{2} } [/tex]
[tex]y = 3[/tex]
a)
[tex]x \times ( \sqrt{8} - \sqrt{2}) = 4 [/tex]
[tex]x \times (2 \sqrt{2} - \sqrt{2} ) = 4[/tex]
[tex]2 \sqrt{2} \times \sqrt{2} = 2 \times 2 = 4[/tex]
b)
[tex] {x}^{2} - y = {(2 \sqrt{2}) }^{2} - 3 [/tex]
[tex] = {2}^{2} \times { \sqrt{2} }^{2} - 3 [/tex]
[tex] = 4 \times 2 - 3[/tex]
[tex] = 5[/tex]
