It is most probably Canada 1995. Quite nice, and medium difficulty problem. Try it!

If $\alpha,\beta,\gamma$ are roots of $x^3-x-1$, then find

\[\frac{\alpha-1}{\alpha+1}+\frac{\beta-1}{\beta+1}+\frac{\gamma-1}{\gamma+1}\]

## Find value using the roots of polynomial

### Find value using the roots of polynomial

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please

Please

**install LaTeX fonts**in your PC for better looking equations,**learn****how to write equations**, and**don't forget**to read Forum Guide and Rules.### Re: Find value using the roots of polynomial

Just use $\sum\alpha=0, \sum\alpha\beta=-1, \alpha\beta\gamma=1$

Every logical solution to a problem has its own beauty.

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**Important**: Please make sure that you have read about the**Rules, Posting Permissions and Forum Language**)### Re: Find value using the roots of polynomial

Remember, one of the main purpose of the forum is to practice writing formal solutions.

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please

Please

**install LaTeX fonts**in your PC for better looking equations,**learn****how to write equations**, and**don't forget**to read Forum Guide and Rules.### Re: Find value using the roots of polynomial

Ow... sorry. Actually its painful I will write formal solutions from now

Every logical solution to a problem has its own beauty.

(

(

**Important**: Please make sure that you have read about the**Rules, Posting Permissions and Forum Language**)### Re: Find value using the roots of polynomial

Post more problems, if you have any.

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please

Please

**install LaTeX fonts**in your PC for better looking equations,**learn****how to write equations**, and**don't forget**to read Forum Guide and Rules.- zadid xcalibured
**Posts:**217**Joined:**Thu Oct 27, 2011 11:04 am**Location:**mymensingh

### Re: Find value using the roots of polynomial

Let $S=\frac{\alpha-1}{\alpha+1}+\frac{\beta-1}{\beta+1}+\frac{\gamma-1}{\gamma+1}$

$S+3=2 (\frac{\alpha}{\alpha+1}+\frac{\beta}{\beta+1}+\frac{\gamma}{\gamma+1})$

$S+3=\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}=2$

I posted in the 1st topic of algebra forum.

$S+3=2 (\frac{\alpha}{\alpha+1}+\frac{\beta}{\beta+1}+\frac{\gamma}{\gamma+1})$

$S+3=\frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2}=2$

I posted in the 1st topic of algebra forum.