Brilliant problem

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sakibtanvir
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Brilliant problem

Unread post by sakibtanvir » Sat May 04, 2013 4:47 pm

Any hint is expected..
*Consider the polynomial $P(x)=x^{3}+3x+1$ with roots $r_{1},r_{2},r_{3}$.
Find the value of $(r_{1}^{2}+r_{1}+1)(r_{2}^{2}+r_{2}+1)(r_{3}^{2}+r_{3}+1)$.
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photon
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Re: Brilliant problem

Unread post by photon » Sun May 05, 2013 2:43 pm

$\displaystyle (r_1^2+r_1+1)(r_2^2+r_2+1)(r_3^2+r_3+1)=\frac{r_1^3-1}{r_1-1}.\frac{r_1^3-1}{r_3-1}.\frac{r_3^3-1}{r_3-1}$
put value of $x^3$ and use Vieta's formula .
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