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Beliebt Algebra >

2x^6+88x^2=30x^4

Lösung

2 x^{6} + 88 x^{2} = 30 x^{4}

Lösung

x = 0, x = 2, x = - 2, x = 11, x = - 11

+1

Dezimale

x = 0, x = 2, x = - 2, x = 3.31662 \dots, x = - 3.31662 \dots

Schritte zur Lösung

2 x^{6} + 88 x^{2} = 30 x^{4}

Verschiebe

30 x^{4}

auf die linke Seite

2 x^{6} + 88 x^{2} - 30 x^{4} = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

2 x^{6} - 30 x^{4} + 88 x^{2} = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}

und

u^{3} = x^{6}

2 u^{3} - 30 u^{2} + 88 u = 0

Löse

2 u^{3} - 30 u^{2} + 88 u = 0 : u = 0, u = 4, u = 11

u = 0, u = 4, u = 11

Setze

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

löse für

x

Löse

x^{2} = 0 : x = 0

Löse

x^{2} = 4 : x = 2, x = - 2

Löse

x^{2} = 11 : x = 11, x = - 11

Die Lösungen sind

x = 0, x = 2, x = - 2, x = 11, x = - 11

Graph

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2 (x + 7) (25 x^{2} - 49) = 0

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x^3-3x^2-9x+11=0

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