Änderungen von Dokument BPE 3.4 Polynomgleichungen

Zusammenfassung

• Seiteneigenschaften (2 geändert, 0 hinzugefügt, 0 gelöscht)

Details

Seiteneigenschaften

Dokument-Autor

...	...	@@ -1,1 +1,1 @@
1		-XWiki.akukin
	1	+XWiki.holgerengels

Inhalt

...	...	@@ -54,39 +54,28 @@
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		-
59		-{{formula}}
60		-\begin{align*}
61		-\square x^3+\square &= 0\\
62		-\square x^3 &=\square\quad \left| :2\\
63		-x^3 &= \square \\
64		-x &= -2
65		-\end{align*}
66		-{{/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}}
67	67	)))
68		-1. ((({{{ }}}
69		-
70		-{{formula}}
	62	+1. ((({{formula}}
71	71	\begin{align*}
72		-2x^3+\square x^2 &= 0 \\
73		-\square (x-\square) &= 0 \left|\left| \text{ SVNP }
74		-\end{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}
75	75	{{/formula}}
76		-
77		-{{formula}}\Rightarrow x_{1,2}=\square; x_3=6{{/formula}}
78	78	)))
79		-1. ((({{{ }}}
80		-
81		-{{formula}}\begin{align*}
82		-x^4+\square x^2+\square &= 0 \quad \left|\left|\text{ Subst.: } x^2:=\square\\
83		-z^2+\square z + \square &= 0 \quad \left|\left|\text{ Mitternachtsformel/abc-Formel } &
	70	+1. ((({{formula}}\begin{align*}
	71	+x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
	72	+z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
84	84	\end{align*}
85	85	{{/formula}}
86	86
87	87	{{formula}}
88	88	\begin{align*}
89		-\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}\\
90	90	z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
91	91	\end{align*}
92	92	{{/formula}}