Änderungen von Dokument BPE 3.4 Polynomgleichungen

Zusammenfassung

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

Details

Seiteneigenschaften

Inhalt

...	...	@@ -54,48 +54,32 @@
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		-
69		-{{formula}}
70		-\begin{align*}
71		-2x^3+\square x^2 &= 0 \\
72		-\square (x-\square) &= 0 \left|\left| \text{ SVNP }
73		-\end{align*}
74		-{{/formula}}
75		-
76		-{{formula}}\Rightarrow x_{1,2}=\square; x_3=6{{/formula}}
	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}}
77	77	)))
78		-1. (((
79		-
80		-{{formula}}\begin{align*}
81		-x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: } & x^2:=\square\\
82		-z^2+\square z + \square &= 0 & \left|\left|\text{ SVNP } &
	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*}
	75	+x^4+\square x^2+\square &= 0 & \left|\left|\text{ Subst.: }x^2:=\square\\
	76	+z^2+\square z + \square &= 0 \left|\left|\text{ SVNP } \\
	77	+z_{1,2}=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
	78	+z_1=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}\\
	79	+\text{Resubst.: } \square := x^2\\
	80	+x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
	81	+x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
83	83	\end{align*}
84		-{{/formula}}
85		-
86		-{{formula}}
87		-\begin{align*}
88		-\Rightarrowz_{1,2}&=\frac{\square\pm\sqrt{\square^2-4\cdot\square\cdot\square}}{2\cdot\square}\\
89		-z_1&=\frac{\square+\square}{\square}; z_2=\frac{\square-\square}{\square}
90		-\end{align*}
91		-{{/formula}}
92		-
93		-{{formula}}
94		-\begin{align*}
95		-&\text{Resubst.: } \square := x^2\\
96		-&x_{1,2}^2=36 \Rightarrow x_{1,2}=\square\\
97		-&x_{3,4}^2=\square \Rightarrow x_{3,4}=\pm 2
98		-\end{align*}
99	99	{{/formula}})))
100	100	{{/aufgabe}}
101	101