Question

Rezolvati in RxR(R patrat) urmatoarele sisteme de ecuatii:
a) y=3x patrat-2x+1
y=3x-1
b)y=2x patrat-3x+2
y=4x-4

Answer 1

a)
y = 3x² - 2x + 2
y = 3x - 1
Prima ecuatie o folosim ca substitutie
3x² - 2x + 2 = 3x - 2
3x² - 5x + 4 = 0

x₁₂ = [5 ± √(25 - 16)] / 6 = [5 ± √9] / 2 = (5 ± 3)/6

x₁ = (5 + 3) / 6 = 8 / 6 = 4 / 3
y₁ = 3x - 1 = 3 * 4/3 - 1 = 4 - 1 = 3
---
x₂ = (5 - 3) / 6 = 2 / 6 = 1 / 3
y₂ = 3x - 1 = 3 * 1/3 -1 = 1 - 1 = 0

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b) 
y = 2x² - 3x + 2
y = 4x - 4
Prima ecuatie o folosim ca substitutie
2x² - 3x + 2 = 4x - 4 
2x² - 3x - 4x +2 + 4 = 0
2x² -7x + 6 = 0

x₁₂ = [7 ± √(49 - 48) ] / 4 
x₁₂ = [7 ± √1] / 4
x₁₂ = (7 ± 1) / 4

x₁ = (7 + 1) / 4 = 2
y₁ = 4x - 4 = 8 - 4 = 4
---
x₂ = (7 - 1) / 4 = 6 / 4 = 3 / 2
y₂ = 4x - 4 = 4 * 3/2 - 4 = 6 - 4 = 2