Änderungen von Dokument BPE 3.4 Polynomgleichungen

Zusammenfassung

• Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)

Details

Seiteneigenschaften

Inhalt

...	...	@@ -59,27 +59,33 @@
59	59	{{formula}}x^3=\square{{/formula}}
60	60	{{formula}}x=-2{{/formula}}
61	61	)))
62		-1. ((({{formula}}2x^3+\square x^2=0{{/formula}}
63		-{{formula}}\square (x-\square)=0{{/formula}} || SVNP
64		-{{formula}}x_{1,2}=\square; x_3=6{{/formula}}
	62	+1. ((({{formula}}
	63	+\begin{align*}
	64	+&2x^3+\square x^2&=0
	65	+&\square (x-\square)&=0 || SVNP
	66	+&x_{1,2}=\square; x_3=6
	67	+\end{*align}
	68	+{{/formula}}
65	65	)))
66		-1. ((({{formula}}x^4+\square x^2+\square=0{{/formula}} || Subst.: {{formula}}x^2:=\square{{/formula}}
67		-{{formula}}z^2+\square z + \square = 0{{/formula}} || SVNP
68		-{{formula fontSize="larger"}}z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}{{/formula}}
69		-{{formula fontSize="larger"}}z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}{{/formula}}
70		-Resubst.: {{formula}}\square := x^2{{/formula}}
71		-{{formula}}x_{1,2}^2=36 \Rightarrow x_{1,2}=\square{{/formula}}
72		-{{formula}}x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2{{/formula}}
73		-)))
74	74	1. ((({{formula}}\begin{align*}
75		-x^4+\square x^2+\square=0 \left|\text{ Subst.: }x^2:=\square\\
76		-z^2+\square z + \square = 0 \text{ SVNP } \\
77		-z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
78		-z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}\\
79		-\text{Resubst.: } \square := x^2\\
80		-x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
81		-x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
	71	+x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
	72	+z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
82	82	\end{align*}
	74	+{{/formula}}
	75	+
	76	+{{formula}}
	77	+\begin{align*}
	78	+z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
	79	+z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
	80	+\end{align*}
	81	+{{/formula}}
	82	+
	83	+{{formula}}
	84	+\begin{align*}
	85	+&\text{Resubst.: } \square := x^2\\
	86	+&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
	87	+&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
	88	+\end{align*}
83	83	{{/formula}})))
84	84	{{/aufgabe}}
85	85