1. ## sqrt(2)-1 = 1/(sqrt(2)+1)

sqrt(2)-1 = 1/(sqrt(2)+1)

Can someone show me how this is possible?

2. Originally Posted by techmath
sqrt(2)-1 = 1/(sqrt(2)+1)

Can someone show me how this is possible?
Multiply by the conjugate:
$(\sqrt{2}-1) \cdot \frac{\sqrt{2}+1}{\sqrt{2}+1} = \ldots$

3. Originally Posted by techmath
sqrt(2)-1 = 1/(sqrt(2)+1)

Can someone show me how this is possible?
Multiply through by $\sqrt2 + 1$

$(\sqrt2 -1)(\sqrt2 +1) = 1$

Note that the left hand side is the difference of two squares

4. Originally Posted by techmath
sqrt(2)-1 = 1/(sqrt(2)+1)

Can someone show me how this is possible?
Note that $\sqrt{2}-1=\left(\sqrt{2}-1\right)\cdot1=\left(\sqrt{2}-1\right)\frac{\sqrt{2}+1}{\sqrt{2}+1}=\frac{\left( \sqrt{2}-1\right)\left(\sqrt{2}+1\right)}{\sqrt{2}+1}=\frac {2-1}{\sqrt{2}+1}$ $=\frac{1}{\sqrt{2}+1}$

Does this make sense?

EDIT: Grr...I'm too slow today... XD