Änderungen von Dokument BPE 3.4 Polynomgleichungen

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

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...	...	@@ -54,34 +54,46 @@
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. ((({{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}}
	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}}
61	61	)))
62		-1. ((({{formula}}2x^3+\square x^2=0{{/formula}}
63		-{{formula}}\square (x-\square)=0{{/formula}} || SVNP
	67	+1. (((
	68	+{{formula}}
	69	+\begin{align*}
	70	+2x^3+\square x^2 &= 0 \\
	71	+\square (x-\square) &= 0 \left|\left| \text{ SVNP }
	72	+\end{align*}
	73	+{{/formula}}
	74	+
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		-1. ((({{formula}}\begin{align*}
	77	+1. (((
	78	+{{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 } &
77	77	\end{align*}
	82	+{{/formula}}
	83	+
	84	+{{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
	86	+z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
	87	+z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
84	84	\end{align*}
	89	+{{/formula}}
	90	+
	91	+{{formula}}
	92	+\begin{align*}
	93	+&\text{Resubst.: } \square := x^2\\
	94	+&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
	95	+&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
	96	+\end{align*}
85	85	{{/formula}})))
86	86	{{/aufgabe}}
87	87