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Beliebt Algebra >

x^4-41x^2+300=0

Lösung

x^{4} - 41 x^{2} + 300 = 0

Lösung

x = \frac{41 + 481}{2}, x = - \frac{41 + 481}{2}, x = \frac{41 - 481}{2}, x = - \frac{41 - 481}{2}

+1

Dezimale

x = 5.60944 \dots, x = - 5.60944 \dots, x = 3.08774 \dots, x = - 3.08774 \dots

Schritte zur Lösung

x^{4} - 41 x^{2} + 300 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - 41 u + 300 = 0

Löse

u^{2} - 41 u + 300 = 0 : u = \frac{41 + 481}{2}, u = \frac{41 - 481}{2}

u = \frac{41 + 481}{2}, u = \frac{41 - 481}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{41 + 481}{2} : x = \frac{41 + 481}{2}, x = - \frac{41 + 481}{2}

Löse

x^{2} = \frac{41 - 481}{2} : x = \frac{41 - 481}{2}, x = - \frac{41 - 481}{2}

Die Lösungen sind

x = \frac{41 + 481}{2}, x = - \frac{41 + 481}{2}, x = \frac{41 - 481}{2}, x = - \frac{41 - 481}{2}

Graph

Beliebte Beispiele

2 x^{3} = 250

64 - 729 x^{3} = 0

x^3-4x^2-3x+10=0

x^{3} - 4 x^{2} - 3 x + 10 = 0

4 x^{3} - 144 x = 0

z^4=16sqrt(3)-16i

z^{4} = 163 - 16 i