Version 6.1 von Kim Fujan am 2025/05/20 13:16

Verstecke letzte Bearbeiter
Kim Fujan 2.1 1 (% class="abc" %)
Kim Fujan 6.1 2 1. {{formula}} x^{2}-2x-3=0 {{/formula}}
Kim Fujan 4.1 3
Kim Fujan 2.1 4 Lösung mit abc-Formel:
Kim Fujan 3.1 5 {{formula}}x_{1,2}=\frac{2\pm \sqrt{4+12}}{2}=\frac{2\pm 4}{2}{{/formula}}
6 {{formula}} x_{1}=3 \quad ; \quad x_{2}=-1 {{/formula}}
Kim Fujan 4.1 7
Kim Fujan 6.1 8 1. {{formula}} e^{2x}-2e^x-3=0 {{/formula}}
Kim Fujan 2.1 9
Kim Fujan 4.1 10 Substitution: {{formula}} e^x=u {{/formula}}
11 {{formula}} u^{2}+2u-3=0 {{/formula}}
12
13 Lösung mit abc-Formel:
14 {{formula}}u_{1,2}=\frac{2\pm \sqrt{4+12}}{2}=\frac{2\pm 4}{2}{{/formula}}
15 {{formula}} u_{1}=3 \quad ; \quad u_{2}=-1 {{/formula}}
Kim Fujan 5.1 16
Kim Fujan 4.1 17 Resubstitution:
18 {{formula}} e^x=3 \quad \Longleftrightarrow \quad x=ln(3) {{/formula}}
19 {{formula}} e^x=-1 \quad \Longleftrightarrow \quad {{/formula}} keine weitere Lösung!
20
Kim Fujan 6.1 21 1. {{formula}} e^x-2e^{\frac{1}{2}x}-3=0 {{/formula}}
Kim Fujan 2.1 22
Kim Fujan 5.1 23 Substitution: {{formula}} e^{\frac{1}{2}x}=u {{/formula}}
24 {{formula}} u^{2}+2u-3=0 {{/formula}}
25
26 Lösung mit abc-Formel:
27 {{formula}}u_{1,2}=\frac{2\pm \sqrt{4+12}}{2}=\frac{2\pm 4}{2}{{/formula}}
28 {{formula}} u_{1}=3 \quad ; \quad u_{2}=-1 {{/formula}}
29
30 Resubstitution:
31 {{formula}} e^{\frac{1}{2}x}=3 \quad \Longleftrightarrow \quad x=2 \cdot ln(3) {{/formula}}
32 {{formula}} e^{\frac{1}{2}x}=-1 \quad \Longleftrightarrow \quad {{/formula}} keine weitere Lösung!
Kim Fujan 6.1 33
Kim Fujan 2.1 34 1. {{formula}} e^x-2-\frac{15}{e^x}}=0 {{/formula}}
35
Kim Fujan 1.1 36 1. {{formula}} 2e^{4x}=e^{2x}+3 {{/formula}}
Kim Fujan 6.1 37 {{formula}} 2e^{4x}-e^{2x}-3=0 {{/formula}}
38
39 Substitution: {{formula}} e^{2x}=u {{/formula}}
40 {{formula}} 2u^{2}-u-3=0 {{/formula}}
41
42 Lösung mit abc-Formel:
43 {{formula}}u_{1,2}=\frac{1\pm \sqrt{1+24}}{2}=\frac{1\pm 5}{2}{{/formula}}
44 {{formula}} u_{1}=3 \quad ; \quad u_{2}=-2 {{/formula}}
45
46 Resubstitution:
47 {{formula}} e^{\frac{1}{2}x}=3 \quad \Longleftrightarrow \quad x=2 \cdot ln(3) {{/formula}}
48 {{formula}} e^{\frac{1}{2}x}=-2 \quad \Longleftrightarrow \quad {{/formula}} keine weitere Lösung!