Question

(1+under root 2)upon (1-under root2)

Answer 1

Answer:

$\frac{1 + \sqrt{2} }{1 - \sqrt{2} } = \frac{1 + \sqrt{2} }{1 - \sqrt{2} } \times \frac{1 + \sqrt{2} }{1 + \sqrt{2} } \\ = \frac{(1 + \sqrt{2} ) {}^{2} }{1 {}^{2} - (\sqrt{2}) {}^{2} } \\ = \frac{1 {}^{2} + ( \sqrt{2} ) {}^{2} + 2 \times \sqrt{2} \times 1}{1 - 2} \\ = \frac{1 + 2 + 2 \sqrt{2} }{ - 1} \\ = - (1 + 2 + 2 \sqrt{2} ) \\ = - 3 - 2 \sqrt{2}$