d) Wzory: ax² + bx + c = 0 Δ = b² - 4ac x1 = (- b - √Δ)/2a x2 = (- b + √Δ)/2a ============= x² + 6x + 9 = 0 Δ = 36 - 36 = 0 x₁ = x₂ = - b/2a = - 6/2 = - 3 e) (x + 1)/3 - x² = 1/2 2(x + 1) - 6x² = 3 - 6x² + 2x + 2 - 3 = 0 - 6x² + 2x - 1 = 0 Δ = 4 - 24 = - 20 równanie nie ma miejsc zerowych f) (2x - 1)/(1 - x) = 1/(2x + 1) (2x - 1)(2x + 1) = 1 - x 4x² - 1 = 1 - x 4x² + x - 2 = 0 Δ = 1 + 32 = 33 √Δ = √33 x₁ = (- 1 - √33)/8 x₂ = (- 1 + √33)/8
[latex]d) x^{2}+6x+9=0\ x^{2}+2*x*3+3^{2}=0\ (x+3)^{2}=0\ x+3=0\ x=-3 -> pierwiastek dwukrotny\ ----------\ e) frac{x+1}{3}-x^{2}=frac{1}{2} |*6\ 2(x+1)-6x^{2}=3\ -6x^{2}+2x+2-3=0\ -6x^{2}+2x-1=0\ Delta=b^{2}-4ac=2^{2}-4*(-6)*(-1)=4-24=-20\ Delta<0 - brak pierwiastkow[/latex] --------------------------------------------------- f) Dziedzina: 1-x≠0 i 2x+1≠0 x=1 x≠-1/2 D={x: x∈R{-1/2, 1}} [latex]frac{2x-1}{1-x}=frac{1}{2x+1}\ (2x-1)(2x+1)=1-x\ 4x^{2}-1+x-1=0\ 4x^{2}+x-2=0\ \ Delta=b^{2}-4ac=1^{2}-4*4*(-2)=1+32=33\ sqrt{Delta}=sqrt{33}\ \ x_{1}=frac{-b-sqrt{Delta}}{2a}=frac{-1-sqrt{33}}{8}\ \ x_{2}=frac{-b+sqrt{Delta}}{2a}=frac{-1+sqrt{33}}{8}[/latex]
