(x)(2x)^2=3.2*10^{-8}

Lösung

(x) (2 x)^{2} = 3.2 \cdot 1 0^{- 8}

x = \frac{1}{500}, x = - \frac{1}{1000} + \frac{3}{1000} i, x = - \frac{1}{1000} - \frac{3}{1000} i

Schritte zur Lösung

(x) (2 x)^{2} = 3.2 \cdot 1 0^{- 8}

Vereinfache

4 x^{3} = \frac{3.2}{100000000}

Teile beide Seiten durch

4

\frac{4 x ^{3}}{4} = \frac{\frac{3.2}{100000000}}{4}

x^{3} = \frac{3.2}{400000000}

Für

x^{3} = f (a)

sind die Lösungen

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

x = 3 \frac{3.2}{400000000}, x = 3 \frac{3.2}{400000000} \frac{- 1 + 3 i}{2}, x = 3 \frac{3.2}{400000000} \frac{- 1 - 3 i}{2}

3 \frac{3.2}{400000000} = \frac{1}{500}

Vereinfache

3 \frac{3.2}{400000000} \frac{- 1 + 3 i}{2} : - \frac{1}{1000} + \frac{3}{1000} i

Vereinfache

3 \frac{3.2}{400000000} \frac{- 1 - 3 i}{2} : - \frac{1}{1000} - \frac{3}{1000} i

x = \frac{1}{500}, x = - \frac{1}{1000} + \frac{3}{1000} i, x = - \frac{1}{1000} - \frac{3}{1000} i

(x + 2) (x^{2} - 2 x + 4) = 0

x^{4} + 4 x^{2} - 45 = 0

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

so l v e f or x, 4 x^{3} - 4 y = 0

- 4 x^{3} = 36 x