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Beliebt Algebra >

10x^4-9x^2+2=0

Lösung

10 x^{4} - 9 x^{2} + 2 = 0

Lösung

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

+1

Dezimale

x = 0.70710 \dots, x = - 0.70710 \dots, x = 0.63245 \dots, x = - 0.63245 \dots

Schritte zur Lösung

10 x^{4} - 9 x^{2} + 2 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

10 u^{2} - 9 u + 2 = 0

Löse

10 u^{2} - 9 u + 2 = 0 : u = \frac{1}{2}, u = \frac{2}{5}

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

Setze

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

löse für

x

Löse

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

Löse

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

Die Lösungen sind

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

Graph

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