Răspuns:
Explicație pas cu pas:
x1+x2 = -1
x1x2 = -a
y1*y2 = x1*x2 = -a
y1 +y2 = x2^3/x1^2 +x1^3/x2^2 =
(x1^5 +x2^5)/(x1^2*x2^2)
(a+b)^5 = a^5 +5a^4b +10a^3b^2 +10a^2b^3 +5ab^4 +b^5
(se tine cont de combinari complementare)
a^5 +b^5 = (a+b)^5 -5ab(a^3 +2a^2b +2ab^2 +b^3)
x1^5 +x2^5 = (-1)^5 +5a(x1^3 -2a(-1) +x2^3 )
x1^3 +x2^3 = (x1+x1)^3 -3x1x2(x1+x2)=
(-1)^3 +3a(-1) = -1 -3a
x1^5 +x2^5 = (-1)^5 +5a(-1 -3a -2a(-1)) =
-1 +5a(-1 -a) = -5a^2 -5a -1
y1 +y2 = -(5a^2 +5a +1)/a^2
Ecuatia:
y^2 +y(5a^2 +5a +1)/a^2 -a = 0
