Polynomial Problem 2

Algebra Level 3

$\alpha,\beta,\gamma$ are the roots of $x^3-x-1=0$ .

Compute $\qquad\qquad\qquad \dfrac{1-\alpha}{1+\alpha} + \dfrac{1-\beta}{1+\beta} + \dfrac{1-\gamma}{1+\gamma}$

1 solution

Robur 131
Oct 2, 2014

From the Equation we get that,

[ I will write alpha, beta, gamma as a,b,c]

a+b+c=0, ab+bc+ca= -1 & abc=1

after some computing we can get to the point,

3+(a+b+c)-(ab+bc+ca)-3abc / 1+ (a+b+c)+(ab+bc+ca)+abc

after plugging in the values we get,

3+0-(-1)-3.1/ 1+0+(-1)+1 =3+1-3/1 =4-3/1= 1/1=1

hey explain me "some computing"

Rishabh Jain - 6 years, 8 months ago

hey explain me too "some computing"

Nihar Mahajan - 6 years, 5 months ago