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Beliebt Algebra >

x^4-5x^2+2=0

Lösung

x^{4} - 5 x^{2} + 2 = 0

Lösung

x = \frac{5 + 17}{2}, x = - \frac{5 + 17}{2}, x = \frac{5 - 17}{2}, x = - \frac{5 - 17}{2}

+1

Dezimale

x = 2.13577 \dots, x = - 2.13577 \dots, x = 0.66215 \dots, x = - 0.66215 \dots

Schritte zur Lösung

x^{4} - 5 x^{2} + 2 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 5 u + 2 = 0

Löse

u^{2} - 5 u + 2 = 0 : u = \frac{5 + 17}{2}, u = \frac{5 - 17}{2}

u = \frac{5 + 17}{2}, u = \frac{5 - 17}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{5 + 17}{2} : x = \frac{5 + 17}{2}, x = - \frac{5 + 17}{2}

Löse

x^{2} = \frac{5 - 17}{2} : x = \frac{5 - 17}{2}, x = - \frac{5 - 17}{2}

Die Lösungen sind

x = \frac{5 + 17}{2}, x = - \frac{5 + 17}{2}, x = \frac{5 - 17}{2}, x = - \frac{5 - 17}{2}

Graph

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5^2x-3-2(x^5)^2=5^2x^3

5^{2} x - 3 - 2 (x^{5})^{2} = 5^{2} x^{3}

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4 x + 3 = x^{3} + 3 x^{2} - 9 x + 12

4 x^{4} + 2 x^{2} + 1 = 0