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Beliebt Algebra >

8x^6-7x^2=0

Lösung

8 x^{6} - 7 x^{2} = 0

Lösung

x = 0, x = - \frac{7}{2 2}, x = - - \frac{7}{2 2}, x = \frac{7}{4 2 ^{3}}, x = - \frac{7}{4 2 ^{3}}

Schritte zur Lösung

8 x^{6} - 7 x^{2} = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{3} = x^{6}

8 u^{3} - 7 u = 0

Löse

8 u^{3} - 7 u = 0 : u = 0, u = - \frac{7}{2 2}, u = \frac{7}{2 2}

u = 0, u = - \frac{7}{2 2}, u = \frac{7}{2 2}

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = 0 : x = 0

Löse

x^{2} = - \frac{7}{2 2} : x = - \frac{7}{2 2}, x = - - \frac{7}{2 2}

Löse

x^{2} = \frac{7}{2 2} : x = \frac{7}{4 2 ^{3}}, x = - \frac{7}{4 2 ^{3}}

Die Lösungen sind

x = 0, x = - \frac{7}{2 2}, x = - - \frac{7}{2 2}, x = \frac{7}{4 2 ^{3}}, x = - \frac{7}{4 2 ^{3}}

Graph

Beliebte Beispiele

x^{3} = 2 x^{2} - x

x^{3} + x^{2} + 3 x - 5 = 0

10-4w^7=7(w+2)6

10 - 4 w^{7} = 7 (w + 2) 6

x^{3} - x = 2

x^{3} - x = - 1