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Zuletzt geändert von Kim Fujan am 2025/05/20 16:21
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1 (%class="abc"%)
2 1. (((
3 (%class="border slim"%)
4 |(%align="center" width="160"%){{formula}}e^{2x}-4e^x+3=0{{/formula}}
5
6 {{formula}}u:=e^x{{/formula}}
7 ⬊|(%align="center" width="160"%){{formula}}x^{2e}-4x^e+3=0{{/formula}}
8
9 {{formula}}u:=x^e{{/formula}}
10 🠗|(%align="center" width="160"%){{formula}}x^{-2}-4x^{-1}+3=0{{/formula}}
11
12 {{formula}}u:=x^{-1}{{/formula}}
13 ⬋
14 ||(%align="center"%){{formula}}u^2-4u+3=0{{/formula}}
15 (((
16
17 {{formula}}u_{1,2}=\frac{4\pm \sqrt{16-12}}{2}{{/formula}}
18 )))
19
20 {{formula}}u_1=3 \quad;\quad u_2=1{{/formula}}|
21 |(%align="center"%)(((⬋
22 {{formula}}e^x:=u{{/formula}}
23 (((
24 {{formula}}x_{1}=ln(3){{/formula}}
25 {{formula}}x_{2}=ln(1)=0{{/formula}}
26
27 )))
28 )))|(%align="center"%)(((🠗
29 {{formula}}x^e:=u{{/formula}}
30 (((
31 {{formula}}x_{1}=\sqrt[e]{3}{{/formula}}
32 {{formula}}x_{2}=\sqrt[e]{1}=1{{/formula}}
33
34 )))
35 )))|(%align="center"%)(((⬊
36 {{formula}}x^{-1}:=u{{/formula}}
37 (((
38 {{formula}}x_{1}=\frac{1}{3}{{/formula}}
39 {{formula}}x_{2}=1{{/formula}}
40
41 )))
42 )))
43 )))
44 1. (((
45 (%class="border slim"%)
46 |(%align="center" width="160"%){{formula}}x^{-2}-3x^{-1}=0{{/formula}}
47
48 {{formula}}u:=x^{-1}_{{/formula}}
49 ⬊|(%align="center" width="160"%){{formula}}x^{2e}-3x^e=0{{/formula}}
50
51 {{formula}}u:=x^e{{/formula}}
52 🠗|(%align="center" width="160"%){{formula}}e^{2x}-3e^x=0{{/formula}}
53
54 {{formula}}u:=e^x{{/formula}}
55 ⬋
56 ||(%align="center"%){{formula}}u^2-3u=0{{/formula}}
57 (((
58
59 {{formula}}u\cdot (u-3)=0{{/formula}}
60 )))
61
62 {{formula}}u_1=0 \quad;\quad u_2=3 {{/formula}}|
63 |(%align="center"%)(((⬋
64 {{formula}}x^{-1}:=u{{/formula}}
65 (((
66 {{formula}}x_{1}=\frac{1}{3}{{/formula}}
67 keine weitere Lösung
68
69 )))
70 )))|(%align="center"%)(((🠗
71 {{formula}}x^e:=u{{/formula}}
72 (((
73 {{formula}}x_{1}=\sqrt[e]{3}{{/formula}}
74 {{formula}}x_{2}=\sqrt[e]{0}=0{{/formula}}
75
76 )))
77 )))|(%align="center"%)(((⬊
78 {{formula}}e^x:=u{{/formula}}
79 (((
80 {{formula}}x_{1}=ln(3){{/formula}}
81 keine weitere Lösung
82 )))
83 )))
84 )))
85 1. (((
86 (%class="border slim"%)
87 |(%align="center" width="160"%){{formula}}x^{-2}-2x^{-1}+3=0{{/formula}}
88
89 {{formula}}u:=x^{-1}{{/formula}}
90 ⬊|(%align="center" width="160"%){{formula}}x^{2e}-2x^e+3=0{{/formula}}
91
92 {{formula}}u:=x^e{{/formula}}
93 🠗|(%align="center" width="160"%){{formula}}e^{2x}-2e^x+3=0{{/formula}}
94
95 {{formula}}u:=e^x{{/formula}}
96 ⬋
97 ||(%align="center"%){{formula}}u^2-2u+3=0{{/formula}}
98 (((
99 {{formula}}u_{1,2}=\frac{2\pm \sqrt{4-12}}{2}{{/formula}}
100
101 keine Lösungen
102
103 )))|
104
105
106 )))