Änderungen von Dokument BPE 3.4 Polynomgleichungen

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

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...	...	@@ -54,28 +54,20 @@
54	54
55	55	{{aufgabe id="Rückwärts lösen" afb="III" kompetenzen="K2,K5" quelle="Martina Wagner" lizenz="BY-SA"}}
56	56	(% class="abc" %)
57		-1. (((
58		-{{formula}}
59		-\begin{align*}
60		-\square x^3+\square &= 0\\
61		-\square x^3 &=\square\quad \left| :2\\
62		-x^3 &= \square \\
63		-x &= -2
64		-\end{align*}
65		-{{/formula}}
	57	+1. ((({{formula}}\square x^3+\square=0{{/formula}}
	58	+{{formula}}\square x^3=\square{{/formula}} | //:2//
	59	+{{formula}}x^3=\square{{/formula}}
	60	+{{formula}}x=-2{{/formula}}
66	66	)))
67		-1. (((
68		-{{formula}}
	62	+1. ((({{formula}}
69	69	\begin{align*}
70		-2x^3+\square x^2 &= 0 \\
71		-\square (x-\square) &= 0 \left|\left| \text{ SVNP }
72		-\end{align*}
	64	+&2x^3+\square x^2&=0 \\
	65	+&\square (x-\square)&=0 \left|\left| \text{ SVNP }\\
	66	+&x_{1,2}=\square; x_3=6
	67	+\end{*align}
73	73	{{/formula}}
74		-
75		-{{formula}}\Rightarrow x_{1,2}=\square; x_3=6{{/formula}}
76	76	)))
77		-1. (((
78		-{{formula}}\begin{align*}
	70	+1. ((({{formula}}\begin{align*}
79	79	x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
80	80	z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
81	81	\end{align*}
...	...	@@ -83,7 +83,7 @@
83	83
84	84	{{formula}}
85	85	\begin{align*}
86		-\Rightarrowz_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
	78	+z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
87	87	z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
88	88	\end{align*}
89	89	{{/formula}}