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Beliebt Algebra >

(25-5x^2)(20-2x^2)-9=0

Lösung

(25 - 5 x^{2}) (20 - 2 x^{2}) - 9 = 0

Lösung

x = \frac{75 + 715}{10}, x = - \frac{75 + 715}{10}, x = \frac{75 - 715}{10}, x = - \frac{75 - 715}{10}

+1

Dezimale

x = 3.18966 \dots, x = - 3.18966 \dots, x = 2.19682 \dots, x = - 2.19682 \dots

Schritte zur Lösung

(25 - 5 x^{2}) (20 - 2 x^{2}) - 9 = 0

Schreibe

(25 - 5 x^{2}) (20 - 2 x^{2}) - 9

um:

10 x^{4} - 150 x^{2} + 491

10 x^{4} - 150 x^{2} + 491 = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

10 u^{2} - 150 u + 491 = 0

Löse

10 u^{2} - 150 u + 491 = 0 : u = \frac{75 + 715}{10}, u = \frac{75 - 715}{10}

u = \frac{75 + 715}{10}, u = \frac{75 - 715}{10}

Setze

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

löse für

x

Löse

x^{2} = \frac{75 + 715}{10} : x = \frac{75 + 715}{10}, x = - \frac{75 + 715}{10}

Löse

x^{2} = \frac{75 - 715}{10} : x = \frac{75 - 715}{10}, x = - \frac{75 - 715}{10}

Die Lösungen sind

x = \frac{75 + 715}{10}, x = - \frac{75 + 715}{10}, x = \frac{75 - 715}{10}, x = - \frac{75 - 715}{10}

Graph

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