25x(10x^{12})=(25x^{10})x^{12}

Lösung

25 x (10 x^{12}) = (25 x^{10}) x^{12}

Lösung

x = 0, x = 910, x = - 9 \frac{5}{256} + i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = - 9 \frac{5}{256} - i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{8 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{8 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{14 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{14 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) - i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{4 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{4 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{10 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{10 π}{9})

Schritte zur Lösung

25 x (10 x^{12}) = (25 x^{10}) x^{12}

Verschiebe

(25 x^{10}) x^{12}

auf die linke Seite

25 x \cdot 10 x^{12} - 25 x^{10} x^{12} = 0

Faktorisiere

25 x \cdot 10 x^{12} - 25 x^{10} x^{12} : - 25 x^{13} (x - 910) (x^{2} + 910 x + 1 0^{\frac{2}{9}}) (x^{6} + 310 x^{3} + 1 0^{\frac{2}{3}})

- 25 x^{13} (x - 910) (x^{2} + 910 x + 1 0^{\frac{2}{9}}) (x^{6} + 310 x^{3} + 1 0^{\frac{2}{3}}) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 910 = 0 or x^{2} + 910 x + 1 0^{\frac{2}{9}} = 0 or x^{6} + 310 x^{3} + 1 0^{\frac{2}{3}} = 0

Löse

x - 910 = 0 : x = 910

Löse

x^{2} + 910 x + 1 0^{\frac{2}{9}} = 0 : x = - 9 \frac{5}{256} + i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = - 9 \frac{5}{256} - i \frac{3 1 0 ^{\frac{2}{9}}}{2}

Löse

x^{6} + 310 x^{3} + 1 0^{\frac{2}{3}} = 0 : x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{8 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{8 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{14 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{14 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) - i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{4 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{4 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{10 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{10 π}{9})

Die Lösungen sind

x = 0, x = 910, x = - 9 \frac{5}{256} + i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = - 9 \frac{5}{256} - i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{8 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{8 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{14 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{14 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) - i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{4 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{4 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{10 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{10 π}{9})

Graph

Beliebte Beispiele

vereinfachen (26/5)/((-5))

s im pl i f y \frac{\frac{26}{5}}{( - 5 )}

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\frac{7.2}{7.5} = \frac{x}{5}

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s im pl i f y (\frac{4}{25})^{\frac{3}{2}}