- #36

FactChecker

Science Advisor

Homework Helper

Gold Member

2023 Award

- 8,802

- 4,267

Absolutely, (I did think that it was an interesting approach though.) Expanding the RHS using the binomial theorem and collection like terms is so methodical that I think I could write a computer program that would generate thousands of such identities.fresh_42 said:I think the detour by the conjugates only makes things more complicated.

It's so much easier to go in that direction than the other way. Consider how hard it would be to go from right to left in this step:

##\frac{1}{2^{10}} (25\sqrt{5}-5\cdot 25+10\cdot 5\sqrt{5}-10\cdot 5+5\cdot \sqrt{5}-1) = \frac{1}{2^{10}} (80\sqrt{5}-176)##