Question

If a =√2+1 and b =√2-1, find 1÷a+1+1÷b+1

Answer 1

$a = \sqrt{2} + 1 \\a + 1 = \sqrt{2} + 2 = \sqrt{2}( \sqrt{2} + 1) \\ b = \sqrt{2} - 1 \\ b + 1 = \sqrt{2} \\ \\ \frac{1}{a + 1} + \frac{1}{b + 1} = \frac{1}{\sqrt{2}( \sqrt{2} + 1)} + \frac{1}{ \sqrt{2} } \\ \\ \frac{1}{a + 1} + \frac{1}{b + 1} = \frac{1 + ( \sqrt{2} + 1)}{\sqrt{2}( \sqrt{2} + 1)} \\ \\ \frac{1}{a + 1} + \frac{1}{b + 1} = \frac{\sqrt{2} + 2}{\sqrt{2}( \sqrt{2} + 1)} = \frac{\sqrt{2}( \sqrt{2} + 1)}{\sqrt{2}( \sqrt{2} + 1)} = 1$

Answer
1