[latex]x^4 - 3x^2 + 2 = 0 \ Podstawiamy: x^2 = t wedge t geq 0 \\ t^2 - 3t + 2 = 0 \ Delta = (-3)^2 - 4 cdot 1 cdot 2 = 9 - 8 = 1 sqrt{Delta} = sqrt{1} = 1 \\ t_1 = frac{3 - 1}{2 cdot 1} = frac{2}{2} = 1 \\ t_2 = frac{3 + 1}{2 cdot 1} = frac{4}{2} = 2 \\ x^2 = 1 vee x^2 = 2 \ x = 1 vee x = - 1 vee x = sqrt{2} vee x = - sqrt{2}[/latex]
x⁴ - 3x² + 2 = 0 podstawię t=x² t² - 3t + 2 =0 a=1 b= -3 c= 2 Δ = b²-4ac = 9-4·1·2 = 1 √Δ = 1 t_1 = (-b-√Δ)/2a = (3-1)/2 = 1 t_2 = (-b+√Δ)/2a = (3+1)/2 = 2 wracamy do iksów pamiętamy że t=x² stąd : x_1 =( -1) x_2= 1 x_3=(-√2) x_4= √2
