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
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
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.
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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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 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.
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
I will write formal solutions from now Every logical solution to a problem has its own beauty.
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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 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.
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.
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zadid xcalibured
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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.