Odpowiedź:
w(x) = x⁴ - 7x² + 6 , u(x) = - x³ + x
x⁴ - 7x² + 6= 0
za x² wstawiam z
z² - 7z + 6 = 0
a = 1 , b = - 7 , c = 6
Δ = b² - 4ac = (- 7)² - 4 * 1 * 6 = 49 - 24 = 25
√Δ = √25 = 5
z₁ = ( - b - √Δ)/2a = (7 - 5)/2 = 2/2 = 1
z₂ = (- b + √Δ)/2a = (7 + 5)/2 = 12/2 = 6
x₁² = 1
x₁² - 1 = 0
(x₁ - 1)(x₁ + 1) = 0
x₁ = 1 ∨ x₁ = - 1
x₂² = 6
(x₂ - √6)(x₂ + √6) = 0
x₂ = √6 ∨ x₂ = - √6
- x³ + x = 0
- x(x² - 1) = 0
- x = 0 ∨ x² - 1 = 0
x = 0 ∨ (x - 1)(x + 1) = 0
x = 0 ∨ x = 1 ∨ x = - 1
W załączniku wykresy funkcji
Z wykresu wynika ,że :
x ∈ ( - 1 , 1 ) ∪ ( 2 , + ∞ )
