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Beliebt Algebra >

4x^4-17x^2+3=0

Lösung

4 x^{4} - 17 x^{2} + 3 = 0

Lösung

x = \frac{17 + 241}{2 2}, x = - \frac{17 + 241}{2 2}, x = \frac{17 - 241}{2 2}, x = - \frac{17 - 241}{2 2}

+1

Dezimale

x = 2.01631 \dots, x = - 2.01631 \dots, x = 0.42950 \dots, x = - 0.42950 \dots

Schritte zur Lösung

4 x^{4} - 17 x^{2} + 3 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

4 u^{2} - 17 u + 3 = 0

Löse

4 u^{2} - 17 u + 3 = 0 : u = \frac{17 + 241}{8}, u = \frac{17 - 241}{8}

u = \frac{17 + 241}{8}, u = \frac{17 - 241}{8}

Setze

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

löse für

x

Löse

x^{2} = \frac{17 + 241}{8} : x = \frac{17 + 241}{2 2}, x = - \frac{17 + 241}{2 2}

Löse

x^{2} = \frac{17 - 241}{8} : x = \frac{17 - 241}{2 2}, x = - \frac{17 - 241}{2 2}

Die Lösungen sind

x = \frac{17 + 241}{2 2}, x = - \frac{17 + 241}{2 2}, x = \frac{17 - 241}{2 2}, x = - \frac{17 - 241}{2 2}

Graph

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