Änderungen von Dokument BPE 3.4 Polynomgleichungen

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...	...	@@ -59,29 +59,34 @@
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
	62	+1. ((({{formula}}
	63	+\begin{align*}
	64	+2x^3+\square x^2 &= 0 \\
	65	+\square (x-\square) &= 0 \left|\left| \text{ SVNP }
	66	+\end{align*}
	67	+{{/formula}}
	68	+
64	64	{{formula}}x_{1,2}=\square; x_3=6{{/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	75	x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
76		-z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &\\
	73	+z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
77	77	\end{align*}
	75	+{{/formula}}
	76	+
	77	+{{formula}}
78	78	\begin{align*}
79		-z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
80		-z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}\\
81		-\text{Resubst.: } \square := x^2\\
82		-x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
83		-x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
	79	+z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
	80	+z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
84	84	\end{align*}
	82	+{{/formula}}
	83	+
	84	+{{formula}}
	85	+\begin{align*}
	86	+&\text{Resubst.: } \square := x^2\\
	87	+&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
	88	+&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
	89	+\end{align*}
85	85	{{/formula}})))
86	86	{{/aufgabe}}
87	87