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Beliebt Algebra >

x^4-1/4-18750x^2=0

Lösung

x^{4} - \frac{1}{4} - 18750 x^{2} = 0

Lösung

x = \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = - \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = \frac{75000 - 7500 0 ^{2} + 16}{8}, x = - \frac{75000 - 7500 0 ^{2} + 16}{8}

Schritte zur Lösung

x^{4} - \frac{1}{4} - 18750 x^{2} = 0

Multipliziere beide Seiten mit

4

4 x^{4} - 75000 x^{2} - 1 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

4 u^{2} - 75000 u - 1 = 0

Löse

4 u^{2} - 75000 u - 1 = 0 : u = \frac{75000 + 7500 0 ^{2} + 16}{8}, u = \frac{75000 - 7500 0 ^{2} + 16}{8}

u = \frac{75000 + 7500 0 ^{2} + 16}{8}, u = \frac{75000 - 7500 0 ^{2} + 16}{8}

Setze

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

löse für

x

Löse

x^{2} = \frac{75000 + 7500 0 ^{2} + 16}{8} : x = \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = - \frac{75000 + 7500 0 ^{2} + 16}{2 2}

Löse

x^{2} = \frac{75000 - 7500 0 ^{2} + 16}{8} : x = \frac{75000 - 7500 0 ^{2} + 16}{8}, x = - \frac{75000 - 7500 0 ^{2} + 16}{8}

Die Lösungen sind

x = \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = - \frac{75000 + 7500 0 ^{2} + 16}{2 2}, x = \frac{75000 - 7500 0 ^{2} + 16}{8}, x = - \frac{75000 - 7500 0 ^{2} + 16}{8}

Graph

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