Răspuns:
X²-mx-1=0
Conform formei reduse a ecuatiei de gradul ll:
p=-m
q=-1
Relatiile lui Viete:
x1x2=q
x1+x2=-p
x1²+x2²=x1+x2+2
(x1+x2)²=x1²+2·x1·x2+x2²
→(x1+x2)²-2·x1·x2=x1+x2+2
x1+x2=-p=-(-m)=m
x1·x2=-1
→ m²-2·(-1)=m+2
m²+2-m-2=0
m²-m=0
m(m-1)=0
m-1=0 sau m=0
m=1 sau m=0
1) m=1
x²-x-1=0
-p=-1 → p=1
q=-1
2)m=0
x²-1=0
p = 0
q=-1
