Änderungen von Dokument BPE 3.4 Polynomgleichungen

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...	...	@@ -63,7 +63,7 @@
63	63	{{formula}}\square (x-\square)=0{{/formula}} || SVNP
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}}
	66	+1. ((({{formula}}x^4+\square x^2+\square=0{{/formula}} || Subst.: {{formula}}x^2\coloneq\square{{/formula}}
67	67	{{formula}}z^2+\square z + \square = 0{{/formula}} || SVNP
68	68	{{formula fontSize="larger"}}z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}{{/formula}}
69	69	{{formula fontSize="larger"}}z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}{{/formula}}
...	...	@@ -71,27 +71,6 @@
71	71	{{formula}}x_{1,2}^2=36 \Rightarrow x_{1,2}=\square{{/formula}}
72	72	{{formula}}x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2{{/formula}}
73	73	)))
74		-1. ((((% style="vertical-align: top" %)
75		-{{formula}}\begin{align*}
76		-x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
77		-z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
78		-\end{align*}
79		-{{/formula}}
80		-
81		-{{formula}}
82		-\begin{align*}
83		-z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
84		-z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
85		-\end{align*}
86		-{{/formula}}
87		-
88		-{{formula}}
89		-\begin{align*}
90		-&\text{Resubst.: } \square := x^2\\
91		-&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
92		-&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
93		-\end{align*}
94		-{{/formula}})))
95	95	{{/aufgabe}}
96	96
97	97	{{aufgabe id="Einfache Ungleichung" afb="I" kompetenzen="K4" quelle="Stefanie Schmidt" lizenz="BY-SA"}}