e=1.6× 10e^{12}

Lösung

e = 1.6 \cdot 10 e^{12}

e = 0, e = \frac{1}{11 16}

Dezimale

e = 0, e = 0.77720 \dots

Schritte zur Lösung

e = 1.6 \cdot 10 e^{12}

Tausche die Seiten

1.6 \cdot 10 e^{12} = e

Verschiebe

e

auf die linke Seite

16 e^{12} - e = 0

Faktorisiere

16 e^{12} - e : e (1116 e - 1) (1 6^{\frac{10}{11}} e^{10} + 1 6^{\frac{9}{11}} e^{9} + 1 6^{\frac{8}{11}} e^{8} + 1 6^{\frac{7}{11}} e^{7} + 1 6^{\frac{6}{11}} e^{6} + 1 6^{\frac{5}{11}} e^{5} + 1 6^{\frac{4}{11}} e^{4} + 1 6^{\frac{3}{11}} e^{3} + 1 6^{\frac{2}{11}} e^{2} + 1116 e + 1)

e (1116 e - 1) (1 6^{\frac{10}{11}} e^{10} + 1 6^{\frac{9}{11}} e^{9} + 1 6^{\frac{8}{11}} e^{8} + 1 6^{\frac{7}{11}} e^{7} + 1 6^{\frac{6}{11}} e^{6} + 1 6^{\frac{5}{11}} e^{5} + 1 6^{\frac{4}{11}} e^{4} + 1 6^{\frac{3}{11}} e^{3} + 1 6^{\frac{2}{11}} e^{2} + 1116 e + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

e = 0 or 1116 e - 1 = 0 or 1 6^{\frac{10}{11}} e^{10} + 1 6^{\frac{9}{11}} e^{9} + 1 6^{\frac{8}{11}} e^{8} + 1 6^{\frac{7}{11}} e^{7} + 1 6^{\frac{6}{11}} e^{6} + 1 6^{\frac{5}{11}} e^{5} + 1 6^{\frac{4}{11}} e^{4} + 1 6^{\frac{3}{11}} e^{3} + 1 6^{\frac{2}{11}} e^{2} + 1116 e + 1 = 0

Löse

1116 e - 1 = 0 : e = \frac{1}{11 16}

Löse

1 6^{\frac{10}{11}} e^{10} + 1 6^{\frac{9}{11}} e^{9} + 1 6^{\frac{8}{11}} e^{8} + 1 6^{\frac{7}{11}} e^{7} + 1 6^{\frac{6}{11}} e^{6} + 1 6^{\frac{5}{11}} e^{5} + 1 6^{\frac{4}{11}} e^{4} + 1 6^{\frac{3}{11}} e^{3} + 1 6^{\frac{2}{11}} e^{2} + 1116 e + 1 = 0 :

Keine Lösung für

e \in R

Die Lösungen sind

e = 0, e = \frac{1}{11 16}

x^{5} - 7 x^{4} + 14 x^{3} - 2 x^{2} - 15 x + 9 = 0

r a t i o na l roo t s t es t x^{4} - 4 x^{3} - x^{2} + 14 x + 10

roo t s x^{4} + x^{2} + 1

x^{3} - 2 x^{2} - 11 x - 12 = 0

z^{6} - (3 + 2 i) z^{3} + 2 + 2 i = 0