Wiki-Quellcode von Lösung Gleichungen gemeinsamer Form
Zuletzt geändert von Kim Fujan am 2025/05/20 16:21
Verstecke letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
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1.1 | 1 | (%class="abc"%) |
| 2 | 1. ((( | ||
| 3 | (%class="border slim"%) | ||
| 4 | |(%align="center" width="160"%){{formula}}e^{2x}-4e^x+3=0{{/formula}} | ||
| 5 | |||
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2.1 | 6 | {{formula}}u:=e^x{{/formula}} |
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1.1 | 7 | ⬊|(%align="center" width="160"%){{formula}}x^{2e}-4x^e+3=0{{/formula}} |
| 8 | |||
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2.1 | 9 | {{formula}}u:=x^e{{/formula}} |
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1.1 | 10 | 🠗|(%align="center" width="160"%){{formula}}x^{-2}-4x^{-1}+3=0{{/formula}} |
| 11 | |||
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2.1 | 12 | {{formula}}u:=x^{-1}{{/formula}} |
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1.1 | 13 | ⬋ |
| 14 | ||(%align="center"%){{formula}}u^2-4u+3=0{{/formula}} | ||
| 15 | ((( | ||
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6.1 | 16 | |
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5.1 | 17 | {{formula}}u_{1,2}=\frac{4\pm \sqrt{16-12}}{2}{{/formula}} |
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1.1 | 18 | ))) |
| 19 | |||
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7.1 | 20 | {{formula}}u_1=3 \quad;\quad u_2=1{{/formula}}| |
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1.1 | 21 | |(%align="center"%)(((⬋ |
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9.1 | 22 | {{formula}}e^x:=u{{/formula}} |
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1.1 | 23 | ((( |
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11.1 | 24 | {{formula}}x_{1}=ln(3){{/formula}} |
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13.6 | 25 | {{formula}}x_{2}=ln(1)=0{{/formula}} |
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1.1 | 26 | |
| 27 | ))) | ||
| 28 | )))|(%align="center"%)(((🠗 | ||
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9.1 | 29 | {{formula}}x^e:=u{{/formula}} |
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1.1 | 30 | ((( |
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12.1 | 31 | {{formula}}x_{1}=\sqrt[e]{3}{{/formula}} |
| 32 | {{formula}}x_{2}=\sqrt[e]{1}=1{{/formula}} | ||
| |
1.1 | 33 | |
| 34 | ))) | ||
| 35 | )))|(%align="center"%)(((⬊ | ||
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9.1 | 36 | {{formula}}x^{-1}:=u{{/formula}} |
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1.1 | 37 | ((( |
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13.1 | 38 | {{formula}}x_{1}=\frac{1}{3}{{/formula}} |
| 39 | {{formula}}x_{2}=1{{/formula}} | ||
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1.1 | 40 | |
| 41 | ))) | ||
| 42 | ))) | ||
| 43 | ))) | ||
| 44 | 1. ((( | ||
| 45 | (%class="border slim"%) | ||
| 46 | |(%align="center" width="160"%){{formula}}x^{-2}-3x^{-1}=0{{/formula}} | ||
| 47 | |||
| |
13.2 | 48 | {{formula}}u:=x^{-1}_{{/formula}} |
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1.1 | 49 | ⬊|(%align="center" width="160"%){{formula}}x^{2e}-3x^e=0{{/formula}} |
| 50 | |||
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13.3 | 51 | {{formula}}u:=x^e{{/formula}} |
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1.1 | 52 | 🠗|(%align="center" width="160"%){{formula}}e^{2x}-3e^x=0{{/formula}} |
| 53 | |||
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13.2 | 54 | {{formula}}u:=e^x{{/formula}} |
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1.1 | 55 | ⬋ |
| 56 | ||(%align="center"%){{formula}}u^2-3u=0{{/formula}} | ||
| 57 | ((( | ||
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13.5 | 58 | |
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13.4 | 59 | {{formula}}u\cdot (u-3)=0{{/formula}} |
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1.1 | 60 | ))) |
| 61 | |||
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13.5 | 62 | {{formula}}u_1=0 \quad;\quad u_2=3 {{/formula}}| |
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1.1 | 63 | |(%align="center"%)(((⬋ |
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13.7 | 64 | {{formula}}x^{-1}:=u{{/formula}} |
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1.1 | 65 | ((( |
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13.7 | 66 | {{formula}}x_{1}=\frac{1}{3}{{/formula}} |
| 67 | keine weitere Lösung | ||
| |
1.1 | 68 | |
| 69 | ))) | ||
| 70 | )))|(%align="center"%)(((🠗 | ||
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13.8 | 71 | {{formula}}x^e:=u{{/formula}} |
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1.1 | 72 | ((( |
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13.9 | 73 | {{formula}}x_{1}=\sqrt[e]{3}{{/formula}} |
| 74 | {{formula}}x_{2}=\sqrt[e]{0}=0{{/formula}} | ||
| |
1.1 | 75 | |
| 76 | ))) | ||
| 77 | )))|(%align="center"%)(((⬊ | ||
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13.7 | 78 | {{formula}}e^x:=u{{/formula}} |
| |
1.1 | 79 | ((( |
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13.9 | 80 | {{formula}}x_{1}=ln(3){{/formula}} |
| 81 | keine weitere Lösung | ||
| |
1.1 | 82 | ))) |
| 83 | ))) | ||
| 84 | ))) | ||
| 85 | 1. ((( | ||
| 86 | (%class="border slim"%) | ||
| 87 | |(%align="center" width="160"%){{formula}}x^{-2}-2x^{-1}+3=0{{/formula}} | ||
| 88 | |||
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13.11 | 89 | {{formula}}u:=x^{-1}{{/formula}} |
| |
1.1 | 90 | ⬊|(%align="center" width="160"%){{formula}}x^{2e}-2x^e+3=0{{/formula}} |
| 91 | |||
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13.11 | 92 | {{formula}}u:=x^e{{/formula}} |
| |
1.1 | 93 | 🠗|(%align="center" width="160"%){{formula}}e^{2x}-2e^x+3=0{{/formula}} |
| 94 | |||
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13.11 | 95 | {{formula}}u:=e^x{{/formula}} |
| |
1.1 | 96 | ⬋ |
| 97 | ||(%align="center"%){{formula}}u^2-2u+3=0{{/formula}} | ||
| 98 | ((( | ||
| |
13.12 | 99 | {{formula}}u_{1,2}=\frac{2\pm \sqrt{4-12}}{2}{{/formula}} |
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13.14 | 100 | |
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14.3 | 101 | keine Lösungen |
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13.15 | 102 | |
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14.3 | 103 | )))| |
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1.1 | 104 | |
| 105 | |||
| 106 | ))) | ||
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14.1 | 107 | |
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1.1 | 108 |