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Beliebt Algebra >

15x^4-11x^2+2=0

Lösung

15 x^{4} - 11 x^{2} + 2 = 0

Lösung

x = \frac{2}{5}, x = - \frac{2}{5}, x = \frac{1}{3}, x = - \frac{1}{3}

+1

Dezimale

x = 0.63245 \dots, x = - 0.63245 \dots, x = 0.57735 \dots, x = - 0.57735 \dots

Schritte zur Lösung

15 x^{4} - 11 x^{2} + 2 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

15 u^{2} - 11 u + 2 = 0

Löse

15 u^{2} - 11 u + 2 = 0 : u = \frac{2}{5}, u = \frac{1}{3}

u = \frac{2}{5}, u = \frac{1}{3}

Setze

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

löse für

x

Löse

x^{2} = \frac{2}{5} : x = \frac{2}{5}, x = - \frac{2}{5}

Löse

x^{2} = \frac{1}{3} : x = \frac{1}{3}, x = - \frac{1}{3}

Die Lösungen sind

x = \frac{2}{5}, x = - \frac{2}{5}, x = \frac{1}{3}, x = - \frac{1}{3}

Graph

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