- Thread starter
- #1
ATroelstein
New member
- Jun 30, 2012
- 15
I have the following equation that I'm trying to simplify:
$$\frac{5 + \sqrt{5}}{2\sqrt{5}}*(\frac{1 + \sqrt{5}}{2})^{x}
$$
From looking at it, it seems like it could be simplified so that the right-hand side of the multiplication would be:
$$(\frac{1 + \sqrt{5}}{2})^{x+1}
$$
I started to pull the left-hand side apart to get a match to the right-hand side and ended up with:
$$
(\frac{4}{2\sqrt{5}} + \frac{1}{\sqrt{5}} * \frac{1+\sqrt{5}}{2}) * (\frac{1 + \sqrt{5}}{2})^{x}
$$
From here, I'm starting to wonder if my initial observation was flawed. Is there a way to simplify this is terms of:
$$(\frac{1 + \sqrt{5}}{2})^{x+1}
$$
Thanks.
$$\frac{5 + \sqrt{5}}{2\sqrt{5}}*(\frac{1 + \sqrt{5}}{2})^{x}
$$
From looking at it, it seems like it could be simplified so that the right-hand side of the multiplication would be:
$$(\frac{1 + \sqrt{5}}{2})^{x+1}
$$
I started to pull the left-hand side apart to get a match to the right-hand side and ended up with:
$$
(\frac{4}{2\sqrt{5}} + \frac{1}{\sqrt{5}} * \frac{1+\sqrt{5}}{2}) * (\frac{1 + \sqrt{5}}{2})^{x}
$$
From here, I'm starting to wonder if my initial observation was flawed. Is there a way to simplify this is terms of:
$$(\frac{1 + \sqrt{5}}{2})^{x+1}
$$
Thanks.