(m-1)^3-2m(m^2-4)<1

Lösung

(m - 1)^{3} - 2 m (m^{2} - 4) < 1

\frac{- 5 - 29}{2} < m < \frac{29 - 5}{2} or m > 2

Intervall-Notation

(\frac{- 5 - 29}{2}, \frac{29 - 5}{2}) \cup (2, \infty)

Dezimale

- 5.19258 \dots < m < 0.19258 \dots or m > 2

Schritte zur Lösung

(m - 1)^{3} - 2 m (m^{2} - 4) < 1

Rewrite in standard form

- m^{3} - 3 m^{2} + 11 m - 2 < 0

Faktor

- m^{3} - 3 m^{2} + 11 m - 2 : - (m - 2) (m - \frac{- 5 + 29}{2}) (m - \frac{- 5 - 29}{2})

- (m - 2) (m - \frac{- 5 + 29}{2}) (m - \frac{- 5 - 29}{2}) < 0

Multipliziere beide Seiten mit

- 1

(drehe die Ungleichung um)

(- (m - 2) (m - \frac{- 5 + 29}{2}) (m - \frac{- 5 - 29}{2})) (- 1) > 0 \cdot (- 1)

Vereinfache

(m - 2) (m - \frac{- 5 + 29}{2}) (m - \frac{- 5 - 29}{2}) > 0

Identifiziere die Intervalle

\frac{- 5 - 29}{2} < m < \frac{29 - 5}{2} or m > 2

5 x^{2} = 2 x + 4

0.1 (0.5 m + 6) = 2

s im pl i f y 5 \cdot \frac{π}{180}

c^{2} = 3^{2} + 8^{2}

R = 7 (0) - 11