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Beliebt Algebra >

7(x^2+3)^2-x^2=0

Lösung

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

Lösung

x = \frac{1}{2 7} + \frac{83}{2 7} i, x = - \frac{1}{2 7} - \frac{83}{2 7} i, x = \frac{1}{2 7} - \frac{83}{2 7} i, x = - \frac{1}{2 7} + \frac{83}{2 7} i

Schritte zur Lösung

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

Schreibe

7 (x^{2} + 3)^{2} - x^{2}

um:

7 x^{4} + 41 x^{2} + 63

7 x^{4} + 41 x^{2} + 63 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

7 u^{2} + 41 u + 63 = 0

Löse

7 u^{2} + 41 u + 63 = 0 : u = - \frac{41}{14} + i \frac{83}{14}, u = - \frac{41}{14} - i \frac{83}{14}

u = - \frac{41}{14} + i \frac{83}{14}, u = - \frac{41}{14} - i \frac{83}{14}

Setze

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

löse für

x

Löse

x^{2} = - \frac{41}{14} + i \frac{83}{14} : x = \frac{1}{2 7} + \frac{83}{2 7} i, x = - \frac{1}{2 7} - \frac{83}{2 7} i

Löse

x^{2} = - \frac{41}{14} - i \frac{83}{14} : x = \frac{1}{2 7} - \frac{83}{2 7} i, x = - \frac{1}{2 7} + \frac{83}{2 7} i

Die Lösungen sind

x = \frac{1}{2 7} + \frac{83}{2 7} i, x = - \frac{1}{2 7} - \frac{83}{2 7} i, x = \frac{1}{2 7} - \frac{83}{2 7} i, x = - \frac{1}{2 7} + \frac{83}{2 7} i

Graph

Beliebte Beispiele

100t^3-50*10^3*t-375*10^3=0

100 t^{3} - 50 \cdot 1 0^{3} \cdot t - 375 \cdot 1 0^{3} = 0

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

0.0004x^4=20x^2

0.0004 x^{4} = 20 x^{2}

x^{10} = 5

solvefor x,x^3-y^3-z^3=4

so l v e f or x, x^{3} - y^{3} - z^{3} = 4