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Beliebt Algebra >

9x^4-40x^2+16=0

Lösung

9 x^{4} - 40 x^{2} + 16 = 0

Lösung

x = 2, x = - 2, x = \frac{2}{3}, x = - \frac{2}{3}

+1

Dezimale

x = 2, x = - 2, x = 0.66666 \dots, x = - 0.66666 \dots

Schritte zur Lösung

9 x^{4} - 40 x^{2} + 16 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

9 u^{2} - 40 u + 16 = 0

Löse

9 u^{2} - 40 u + 16 = 0 : u = 4, u = \frac{4}{9}

u = 4, u = \frac{4}{9}

Setze

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

löse für

x

Löse

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

Löse

x^{2} = \frac{4}{9} : x = \frac{2}{3}, x = - \frac{2}{3}

Die Lösungen sind

x = 2, x = - 2, x = \frac{2}{3}, x = - \frac{2}{3}

Graph

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