Question

1. Rozwiaz algebraicznie ponizszy uklad:

x+y=2

x^2-y=0

Answer 1

x+ y = 2

x²- y = 0 

 

x= 2-y

(2-y)² -y = 0

 

x = 2-y

4 – 4y + y² - y = 0

 

x = 2- y

y² -5y +4 = 0

 

Δ = b² - 4ac = (-5)² - 4 *1*4 = 25-16 = 4

√Δ = √4 = 2

y₁ = (-b-√Δ)/2a = (5-2)/2  = 3/2 = 1i1/2

y₁ = (-b+√Δ)/2a = (5+2)/2  = 7/2 = 3 i1/2

 

gdy:

y₁ = 1 i ½

x=2-y

 

y₁ = 1 i ½

x=2- 1 i ½

 

y₁ = 1 i ½

x= ½

 

gdy :

y₂ = 3 i ½

x=2-y

 

y₂ = 3 i ½

x=2- 3 i ½

 

y₂ = 3 i ½

x=- 1 i 1/2