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Beliebt Algebra >

4x^4-401x^2+100=0

Lösung

4 x^{4} - 401 x^{2} + 100 = 0

Lösung

x = 10, x = - 10, x = \frac{1}{2}, x = - \frac{1}{2}

+1

Dezimale

x = 10, x = - 10, x = 0.5, x = - 0.5

Schritte zur Lösung

4 x^{4} - 401 x^{2} + 100 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

4 u^{2} - 401 u + 100 = 0

Löse

4 u^{2} - 401 u + 100 = 0 : u = 100, u = \frac{1}{4}

u = 100, u = \frac{1}{4}

Setze

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

löse für

x

Löse

x^{2} = 100 : x = 10, x = - 10

Löse

x^{2} = \frac{1}{4} : x = \frac{1}{2}, x = - \frac{1}{2}

Die Lösungen sind

x = 10, x = - 10, x = \frac{1}{2}, x = - \frac{1}{2}

Graph

Beliebte Beispiele

2 x^{3} = 9 x^{2}

(x - 2)^{3} = - 125

4x^3-6x^2=10x-15

4 x^{3} - 6 x^{2} = 10 x - 15

-2x(x^2-5)(x^2+1)=0

- 2 x (x^{2} - 5) (x^{2} + 1) = 0

x^{4} - 7 x^{2} - 5 = 0