The teacher will be very surprised to see your correct solution 😉
2 / 2\ a *(1 - x)*\1 - a*x + a*x / = 1
a*x^2 + b*x + c = 0
D = b^2 - 4 * a * c =
(a + a^2)^2 - 4 * (-a^2) * (-1 - a) = (a + a^2)^2 + 4*a^2*(-1 - a)
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
x = -1 / ((-a + a*x)/x)
-1 + a x1 = ------ a
_______________ / 2 1 + a - \/ -3 + a - 2*a x2 = -------------------------- 2*a
_______________ / 2 1 + a + \/ -3 + a - 2*a x3 = -------------------------- 2*a
sum
_______________ _______________ / 2 / 2 -1 + a 1 + a - \/ -3 + a - 2*a 1 + a + \/ -3 + a - 2*a 0 + ------ + -------------------------- + -------------------------- a 2*a 2*a
=
_______________ _______________ / 2 / 2 -1 + a 1 + a + \/ -3 + a - 2*a 1 + a - \/ -3 + a - 2*a ------ + -------------------------- + -------------------------- a 2*a 2*a
product
_______________ _______________ / 2 / 2 -1 + a 1 + a - \/ -3 + a - 2*a 1 + a + \/ -3 + a - 2*a 1*------*--------------------------*-------------------------- a 2*a 2*a
=
2 -1 + a ------- 3 a
(-1 + a^2)/a^3