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Beliebt Algebra >

52x^6=x-23x

Lösung

52 x^{6} = x - 23 x

Lösung

x = 0, x = - 5 \frac{11}{26}

+1

Dezimale

x = 0, x = - 0.84194 \dots

Schritte zur Lösung

52 x^{6} = x - 23 x

Subtrahiere

x - 23 x

von beiden Seiten

52 x^{6} - (x - 23 x) = x - 23 x - (x - 23 x)

Vereinfache

52 x^{6} + 22 x = 0

Faktorisiere

52 x^{6} + 22 x : 2 x (526 x + 511) (2 6^{\frac{4}{5}} x^{4} - 511 \cdot 2 6^{\frac{3}{5}} x^{3} + 28 6^{\frac{2}{5}} x^{2} - 1 1^{\frac{3}{5}} 526 x + 1 1^{\frac{4}{5}})

2 x (526 x + 511) (2 6^{\frac{4}{5}} x^{4} - 511 \cdot 2 6^{\frac{3}{5}} x^{3} + 28 6^{\frac{2}{5}} x^{2} - 1 1^{\frac{3}{5}} 526 x + 1 1^{\frac{4}{5}}) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 526 x + 511 = 0 or 2 6^{\frac{4}{5}} x^{4} - 511 \cdot 2 6^{\frac{3}{5}} x^{3} + 28 6^{\frac{2}{5}} x^{2} - 1 1^{\frac{3}{5}} 526 x + 1 1^{\frac{4}{5}} = 0

Löse

526 x + 511 = 0 : x = - 5 \frac{11}{26}

Löse

2 6^{\frac{4}{5}} x^{4} - 511 \cdot 2 6^{\frac{3}{5}} x^{3} + 28 6^{\frac{2}{5}} x^{2} - 1 1^{\frac{3}{5}} 526 x + 1 1^{\frac{4}{5}} = 0 :

Keine Lösung für

x \in R

Die Lösungen sind

x = 0, x = - 5 \frac{11}{26}

Graph

Beliebte Beispiele

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