Question

Rezolvaţi ecuaţiile folosind relaţiile lu Viete: X2-3x+2=0 ;
x2+4x+3=0; x2-10x+21=0; x2+10x+24=0.

Answer 1

x2-3x+2=0 
x₁+x₂=3
x₁ × x₂=2

x₁=3-x₂
(3-x₂) × x₂=2
3x₂-x₂²-2=0
x₂²-3x₂+2=0
(x₂-1)(x₂-2)=0
x₂=1
x₂=2

x₁=3-1=2
x₁=3-2=1


x2+4x+3=0
x₁+x₂=-4
x₁ × x₂=3

x₁=-4-x₂
(-4-x₂) × x₂=3
-4x₂-x₂²-3=0
x₂²+4x₂+3=0
(x₂+1)(x₂+3)=0
x₂=-1
x₂=-3

x₁=-4+1=-3
x₁=-4+3=-1

x2-10x+21=0
x₁+x₂=10
x₁ × x₂=21

x₁=10-x₂
(10-x₂) × x₂=21
10x₂-x₂²-21=0
x₂²-10x₂+21=0
(x₂-7)(x₂-3)=0
x₂=7
x₂=3

x₁=10-7=3
x₁=10-3=7

x2+10x+24=0
x₁+x₂=-10
x₁ × x₂=24

x₁=-10-x₂
(-10-x₂) × x₂=24
-10x₂-x₂²-24=0
x₂²+10x₂+24=0
(x₂+4)(x₂+6)=0
x₂=-4
x₂=-6

x₁=-10+4=-6
x₁=-10+6=-4