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Beliebt Algebra >

x^8+35x^4=36

Lösung

x^{8} + 35 x^{4} = 36

Lösung

x = 1, x = - 1, x = i, x = - i, x = 3 + 3 i, x = - 3 - 3 i, x = 3 - 3 i, x = - 3 + 3 i

Schritte zur Lösung

x^{8} + 35 x^{4} = 36

Verschiebe

36

auf die linke Seite

x^{8} + 35 x^{4} - 36 = 0

Schreibe die Gleichung um mit

u = x^{2}, u^{2} = x^{4}

und

u^{4} = x^{8}

u^{4} + 35 u^{2} - 36 = 0

Löse

u^{4} + 35 u^{2} - 36 = 0 : u = 1, u = - 1, u = 6 i, u = - 6 i

u = 1, u = - 1, u = 6 i, u = - 6 i

Setze

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

löse für

x

Löse

x^{2} = 1 : x = 1, x = - 1

Löse

x^{2} = - 1 : x = i, x = - i

Löse

x^{2} = 6 i : x = 3 + 3 i, x = - 3 - 3 i

Löse

x^{2} = - 6 i : x = 3 - 3 i, x = - 3 + 3 i

Die Lösungen sind

x = 1, x = - 1, x = i, x = - i, x = 3 + 3 i, x = - 3 - 3 i, x = 3 - 3 i, x = - 3 + 3 i

Graph

Beliebte Beispiele

x(3x^2-2x-12x+8)=0

x (3 x^{2} - 2 x - 12 x + 8) = 0

solvefor x,x^3+y^3+z^3=1

so l v e f or x, x^{3} + y^{3} + z^{3} = 1

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

x^3+5x^2+8x+3=0

x^{3} + 5 x^{2} + 8 x + 3 = 0

solvefor x,9x^4+6y^3=8

so l v e f or x, 9 x^{4} + 6 y^{3} = 8