Question

Fie ecuatia de gradul II: x²-2x+3=0. Sa se calculeze : a) x1²+x2² 

Answer 1

a)x1²+x2²=(x1+x2)²-2x1x2
   dupa Viette
x1+x2=2 si x1x2=3
deci x1²+x²=2²-2*3=4-6=-2
b)$\frac{ x_{1} }{ x_{2} }+ \frac{ x_{2} }{ x_{1} } = \frac{ x_{1}^2+ x_{2}^2 }{ x_{1} x_{2} }= \frac{-2}{3}$
c)$\frac{ x_{1}+ x_{2} }{ x_{1} } + \frac{ x_{1} + x_{2} }{ x_{2} }= \frac{ x_{1} x_{2}+ x_{2}^2+ x_{1}^2+ x_{1} x_{2} }{ x_{1} x_{2} }= \frac{2*3+2}{3}= \frac{8}{3}$

Answer 2

Aici este si b si c sper ca te va ajuta