Rozwiaz uklady rownan. Uklady 2 stopnia . y=x2+2x-3 y=3x-3 X2+1=y X2+2x+y=3

1) [latex]y=x^2+2x-3\ y=3x-3\ \3x-3=x^2+2x-3\ x^2-x=0\ x(x-1)=0\ x=0 x=1[/latex] 2) [latex]x^2+1=y\ x^2+2x+y=3\ \ x^2+2x+x^2+1=3\ 2x^2+2x-2=0/:2\ x^2+x-1=0\ Delta=5\ x_1= frac{-1+ sqrt{5}}{2} x_2= frac{-1- sqrt{5}}{2} [/latex]

zad 1 y = x² + 2x - 3 y = 3x - 3 x² + 2x - 3 = 3x - 3 x² + 2x - 3 - 3x + 3 = 0 x² - x = 0 Δ = (- 1)² - 4 * 1 * 0 = 1 √Δ = √1 = 1 x₁ = (1 - 1)/2 = 0/2 = 0 x₂ = (1 + 1)/2 = 2/2 = 1 y₁ = 3x₁ - 3 = 3 * 0 - 3 = - 3 y₂ = 3x₂ - 3 = 3 * 1 - 3 = 3 - 3 = 0 zad 2 x² + 1 = y x² + 2x + y = 3 stąd y = - x² - 2x + 3 x² + 1 = - x² - 2x + 3 x² + x² + 2x + 1 -3 = 0 2x² + 2x -2 = 0 Δ = 2² - 4 * 2 * (- 2) = 4 + 16 = 20 √Δ = √20 = 4√5 x₁ = (- 2 - 4√5)/4 = 2(- 1 - 2√5)/4 = (- 1 - 2√5)/2 = -(1 + 2√5)/2 x₂ = (- 2 + 4√5)/4 = 2(- 1 + 2√5)/4 = (- 1 + 2√5)/2 y₁ = x₁² + 1 = [- (1 + 2√5)/2]² + 1 = [(1 + 4√5 + 20)]/4 + 1 = (21 + 4√5)/4 + 1 = = (21 + 4√5 + 4)/4 = (25 + 4√5)/4 y₂ = [(- 1 + 2√5)/2]² + 1 = (1 - 4√5 + 20)/4 + 1 = (21 - 4√5)/4 + 1 =  = (21 - 4√5 + 4)/4 = (25 - 4√5)/4