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Beliebt Algebra >

(p^8)^2=p^{10}

Lösung

(p^{8})^{2} = p^{10}

Lösung

p = 0, p = 1, p = - 1, p = \frac{1}{2} + \frac{3}{2} i, p = - \frac{1}{2} - \frac{3}{2} i, p = \frac{1}{2} - \frac{3}{2} i, p = - \frac{1}{2} + \frac{3}{2} i

Schritte zur Lösung

(p^{8})^{2} = p^{10}

Schreibe

(p^{8})^{2}

um:

p^{16}

p^{16} = p^{10}

Verschiebe

p^{10}

auf die linke Seite

p^{16} - p^{10} = 0

Schreibe die Gleichung um mit

u = p^{2}, u^{5} = p^{10}

und

u^{8} = p^{16}

u^{8} - u^{5} = 0

Löse

u^{8} - u^{5} = 0 : u = 0, u = 1, u = - \frac{1}{2} + \frac{3}{2} i, u = - \frac{1}{2} - \frac{3}{2} i

u = 0, u = 1, u = - \frac{1}{2} + \frac{3}{2} i, u = - \frac{1}{2} - \frac{3}{2} i

Setze

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

löse für

p

Löse

p^{2} = 0 : p = 0

Löse

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

Löse

p^{2} = - \frac{1}{2} + \frac{3}{2} i : p = \frac{1}{2} + \frac{3}{2} i, p = - \frac{1}{2} - \frac{3}{2} i

Löse

p^{2} = - \frac{1}{2} - \frac{3}{2} i : p = \frac{1}{2} - \frac{3}{2} i, p = - \frac{1}{2} + \frac{3}{2} i

Die Lösungen sind

p = 0, p = 1, p = - 1, p = \frac{1}{2} + \frac{3}{2} i, p = - \frac{1}{2} - \frac{3}{2} i, p = \frac{1}{2} - \frac{3}{2} i, p = - \frac{1}{2} + \frac{3}{2} i

Graph

Beliebte Beispiele

50=4x^3-44x^2+120x

50 = 4 x^{3} - 44 x^{2} + 120 x

2 x^{3} + 6 x = 1

v^{3} + 1 = 0

-2x^3-3x^2-15x+11=0

- 2 x^{3} - 3 x^{2} - 15 x + 11 = 0

solvefor x,2x^3-2y^3=-3

so l v e f or x, 2 x^{3} - 2 y^{3} = - 3