Änderungen von Dokument BPE 3.4 Polynomgleichungen

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...	...	@@ -59,18 +59,14 @@
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 \left|\left| 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	75	x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
76	76	z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
...	...	@@ -79,16 +79,16 @@
79	79
80	80	{{formula}}
81	81	\begin{align*}
82		-z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
83		-z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}\\
	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}
84	84	\end{align*}
85	85	{{/formula}}
86	86
87	87	{{formula}}
88	88	\begin{align*}
89		-\text{Resubst.: } \square := x^2\\
90		-x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
91		-x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
	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
92	92	\end{align*}
93	93	{{/formula}})))
94	94	{{/aufgabe}}