Odpowiedź:
1.
y = x² - 7x + 1
y = - x² + 2x - 9
x² - 7x + 1 = - x² + 2x - 9
x² + x² - 7x - 2x + 1 + 9 = 0
2x² - 9x + 10 = 0
a = 2 , b = - 9 , c = 10
Δ = b² - 4ac = (- 9)² - 4 * 2 * 10 = 81 - 80 =1
√Δ = √1 = 1
x₁ = (- b - √Δ)/2a = (9 - 1)/4 = 8/4 = 2
x₂ = (- b + √Δ)/2a = (9 + 1)/4 = 10/4 = 2 2/4 = 2 1/2 = 2,5
Istnieje para liczb : x₁ = 2 , x₂ = 2,5
2.
y = - 3x² + x + 1
y = x² + 5x - 23
- 3x² + x + 1 = x² + 5x - 23
- 3x² - x² + x - 5x + 1 + 23 = 0
- 4x² - 4x + 24 = 0
a = - 4 , b = - 4 , c = 24
Δ = b² - 4ac = (- 4)² - 4 * (- 4) * 24 = 16 + 384 = 400
√Δ = √400 = 20
x₁ = (- b - √Δ)/2a = (4 - 20)/(- 8) = - 16/(- 8) = 16/8 = 2
x₂ = (- b + √Δ)/2a = (4 + 20)/(- 8) = 24/(- 8) = - 24/8 = - 3
Istnieje para liczb : x₁ = 2 , x₂ = - 3