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.holgerengels
	1	+XWiki.akukin

Inhalt

...	...	@@ -54,33 +54,39 @@
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	+
	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}}
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}}
	68	+1. ((({{{ }}}
	69	+
	70	+{{formula}}
	71	+\begin{align*}
	72	+2x^3+\square x^2 &= 0 \\
	73	+\square (x-\square) &= 0 \left|\left| \text{ SVNP }
	74	+\end{align*}
	75	+{{/formula}}
	76	+
	77	+{{formula}}\Rightarrow 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. ((((% style="vertical-align: top" %)
	79	+1. ((({{{ }}}
	80	+
75	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 } &
	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 } &
78	78	\end{align*}
79	79	{{/formula}}
80	80
81	81	{{formula}}
82	82	\begin{align*}
83		-z_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
	89	+\Rightarrowz_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
84	84	z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
85	85	\end{align*}
86	86	{{/formula}}