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Beliebt Algebra >

x^4-ax^2+b=0

Lösung

x^{4} - a x^{2} + b = 0

Lösung

x = \frac{a + a ^{2} - 4 b}{2}, x = - \frac{a + a ^{2} - 4 b}{2}, x = \frac{a - a ^{2} - 4 b}{2}, x = - \frac{a - a ^{2} - 4 b}{2}

Schritte zur Lösung

x^{4} - a x^{2} + b = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

u^{2} - a u + b = 0

Löse

u^{2} - a u + b = 0 : u = \frac{a + a ^{2} - 4 b}{2}, u = \frac{a - a ^{2} - 4 b}{2}

u = \frac{a + a ^{2} - 4 b}{2}, u = \frac{a - a ^{2} - 4 b}{2}

Setze

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

löse für

x

Löse

x^{2} = \frac{a + a ^{2} - 4 b}{2} : x = \frac{a + a ^{2} - 4 b}{2}, x = - \frac{a + a ^{2} - 4 b}{2}

Löse

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

Die Lösungen sind

x = \frac{a + a ^{2} - 4 b}{2}, x = - \frac{a + a ^{2} - 4 b}{2}, x = \frac{a - a ^{2} - 4 b}{2}, x = - \frac{a - a ^{2} - 4 b}{2}

Graph

Beliebte Beispiele

Z^{56} = 498

solvefor y,x=8y^3

so l v e f or y, x = 8 y^{3}

4x^3-2x^2+x+7=0

4 x^{3} - 2 x^{2} + x + 7 = 0

- x^{5} + 16 x = 0

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