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