Potenzgleichung... < Klassen 8-10 < Schule < Mathe < Vorhilfe
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(Frage) beantwortet  | | Datum: | 19:00 Sa 05.12.2009 | | Autor: | Lilly007 |
| Aufgabe | | [mm] 2x^3 [/mm] - [mm] x^{\bruch{3}{2}} [/mm] = 0 |
Hab diese Aufgabe gerechnet... Könnte das jemand für mich kontrollieren?
[mm] 2x^3 [/mm] - [mm] x^{\bruch{3}{2}} [/mm] = 0
[mm] 2x^3 [/mm] = [mm] x^{\bruch{3}{2}} [/mm]
[mm] (2x^3)^2 [/mm] = [mm] (x^{\bruch{3}{2}})^2
[/mm]
[mm] 4x^6 [/mm] = [mm] x^{\bruch{6}{2}}
[/mm]
[mm] 4x^6 [/mm] = [mm] x^3
[/mm]
[mm] 4x^6 [/mm] - [mm] x^3 [/mm] = 0
[mm] x^3(4x^3 [/mm] - 1) = 0
[mm] x^3 [/mm] = 0
x = 0
[mm] 4x^3 [/mm] - 1 = 0
[mm] 4x^3 [/mm] = 1
[mm] x^3 [/mm] = [mm] ^{\bruch{1}{4}} [/mm]
x = [mm] \wurzel[3]{{\bruch{1}{4}} }
[/mm]
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Hallo,
> [mm]2x^3[/mm] - [mm]x^{\bruch{3}{2}}[/mm] = 0
> Hab diese Aufgabe gerechnet... Könnte das jemand für
> mich kontrollieren?
>
> [mm]2x^3[/mm] - [mm]x^{\bruch{3}{2}}[/mm] = 0
> [mm]2x^3[/mm] = [mm]x^{\bruch{3}{2}}[/mm]
> [mm](2x^3)^2[/mm] = [mm](x^{\bruch{3}{2}})^2[/mm]
> [mm]4x^6[/mm] = [mm]x^{\bruch{6}{2}}[/mm]
> [mm]4x^6[/mm] = [mm]x^3[/mm]
> [mm]4x^6[/mm] - [mm]x^3[/mm] = 0
> [mm]x^3(4x^3[/mm] - 1) = 0
>
> [mm]x^3[/mm] = 0
> x = 0
>
>
> [mm]4x^3[/mm] - 1 = 0
> [mm]4x^3[/mm] = 1
> [mm]x^3[/mm] = [mm]^{\bruch{1}{4}}[/mm]
> x = [mm]\wurzel[3]{{\bruch{1}{4}} }[/mm]
>
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![[hut]](/images/smileys/hut.gif "[hut]") Gruß
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