Question

Doar 4 si 6 va rog. Multumesc!

Answer 1

Ai rezolvarea in poza.

Answer 2

4. x²-2x+3=0

Relatiile lui Viete: x₁+x₂=-b/a=2

                              x₁x₂=c/a=3

a)(x₁+x₂)²=x₁²+x₂²+2x₁x₂=>x₁²+x₂²=(x₁+x₂)²-2x₁x₂=2²-2*3=4-6=-2

b)x₁/x₂+x₂/x1=(x₁²+x₂²)/x₁x₂=-2/3

c)(x₁+x₂)/x₁+(x₁+x₂)/x₂=(x₁+x₂²+x₁²+x₂)/x₁x₂=(x₂²+x₁²+x₂+x₁)/x₁x₂=(-2+2)/3=0

d)(x₁²+x₂²)(x₁+x₂)=x₁³+x₁²x₂+x₂²x₁+x₂³=>x₁³+x₂²=(x₁²+x₂²)(x₁+x₂)-(x₁+x₂)(x₁²+x₂²)=0

e)x₁²/x₂+x₂²/x₁=(x₁²x₂+x₂²x₁)x₁x₂=(x₁+x₂)(x₁²+x₂²)/x₁x₂=-4/3

6. x²-mx+2=0

S=-m

P=2

S²-2P=0<=>m²-4=0=>m²=4=>m=√4

m₁=-2

m₂=2

m∈{-2;2}