Root3: Rewrite & Produce Non-trivial Equation + Show Irrationality

[flying2000]

1)write root(3)-1 in another way,and use this to produce a non-trivial equation for root(3) in terms of itself

2)suppose m,n(m,n is natural numbers) are such that m/n=root(3),use (1) to write root(3)as another combination of m and n.
3)use (2) to show that root(3) in not rational.

Any hints appreciated..

 

[Tide]

How about

$$\sqrt 3 - 1 = \frac {2}{1+\sqrt 3}$$?

 

[HallsofIvy]

Which, I think, would then give $x- 1= \frac{2}{x+1}$ as a non-trivial equation for $\sqrt{3}$.

If $\frac{m}{n}= \sqrt{3}$, then $\frac{m}{n}-1= \frac{2}{\frac{m}{n}+1}$. Does that lead to anything?

 

[danne89]

Hmm. How do you define non-trivial?

 

[flying2000]

thanx a lot!

thanks a lot to all you guys!
really appreciated..

Which, I think, would then give $x- 1= \frac{2}{x+1}$ as a non-trivial equation for $\sqrt{3}$.

If $\frac{m}{n}= \sqrt{3}$, then $\frac{m}{n}-1= \frac{2}{\frac{m}{n}+1}$. Does that lead to anything?

 

[HallsofIvy]

I would consider anything other than $x= \sqrt{3}$ to be "non-trivial"!

 

[flying2000]

Another question

I would consider anything other than $x= \sqrt{3}$ to be "non-trivial"!

root(3)=(m+3n)/(m+n), if m,n is allowed having the common factor,Does it lead to any contradiction?

 

[integra]

i was wondering wut the answer would be for question 3) for general knowledge