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Beliebt Algebra >

10x^9=7x

Lösung

10 x^{9} = 7 x

Lösung

x = 0, x = - 8 \frac{7}{10}, x = 8 \frac{7}{10}, x = - 4 \frac{7}{10}, x = - - 4 \frac{7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}

Schritte zur Lösung

10 x^{9} = 7 x

Verschiebe

7 x

auf die linke Seite

10 x^{9} - 7 x = 0

Faktorisiere

10 x^{9} - 7 x : x (810 x + 87) (810 x - 87) (410 x^{2} + 47) (410 x^{2} + 2^{\frac{5}{8}} 835 x + 47) (410 x^{2} - 2^{\frac{5}{8}} 835 x + 47)

x (810 x + 87) (810 x - 87) (410 x^{2} + 47) (410 x^{2} + 2^{\frac{5}{8}} 835 x + 47) (410 x^{2} - 2^{\frac{5}{8}} 835 x + 47) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 810 x + 87 = 0 or 810 x - 87 = 0 or 410 x^{2} + 47 = 0 or 410 x^{2} + 2^{\frac{5}{8}} 835 x + 47 = 0 or 410 x^{2} - 2^{\frac{5}{8}} 835 x + 47 = 0

Löse

810 x + 87 = 0 : x = - 8 \frac{7}{10}

Löse

810 x - 87 = 0 : x = 8 \frac{7}{10}

Löse

410 x^{2} + 47 = 0 : x = - 4 \frac{7}{10}, x = - - 4 \frac{7}{10}

Löse

410 x^{2} + 2^{\frac{5}{8}} 835 x + 47 = 0 : x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}

Löse

410 x^{2} - 2^{\frac{5}{8}} 835 x + 47 = 0 : x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}

Die Lösungen sind

x = 0, x = - 8 \frac{7}{10}, x = 8 \frac{7}{10}, x = - 4 \frac{7}{10}, x = - - 4 \frac{7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = - \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} + i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}, x = \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10} - i \frac{2 ^{\frac{3}{8}} \cdot 5 ^{\frac{7}{8}} 8 7}{10}

Graph

Beliebte Beispiele

10x^9-9x^{10}=0.75

10 x^{9} - 9 x^{10} = 0.75

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wurzeln von x^3+1

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x^7-x^4-x^3+1=0

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