(x³+1)+(-2x²-2x)=(x+1)*(x²-x+1)-2x*(x+1)=...=(x+1)*(x²-3x+1)
radacinile polinomului sunt
x1=-1
x2=(3-√5)2
x3=(3+√5)/2
____________
x1*x2=(-3+√5)/2 =>1/x1x2=2/(-3+√5)
x2*x3=x2*x3= (3-√5)*(3+√5)=1=> x2=1/x3
x1*x3=-1*(3+√5)/2=-(3+√5)/2 1/x1*x3=- 2/(3+√5)
Faci inlocuirile
2/(-3+√5)+1-2/(3+√5)=a*[(-3-√5)/2+1+(-3+√5)/2]
aduci la acelasi numitor si faci calculele
(-6-2√5)/(5-9)+1+(6-2√5)(5-9)=a(-3+1)
(3+√5)/2+1+(3-√5)/2=-2a
3+1=-2a
a=-2
