What is (m-1)^3-2m(m^2-4)<1 ?

The solution to (m-1)^3-2m(m^2-4) 2

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

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

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

Interval Notation

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

Decimal Notation

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

Solution steps

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

Rewrite in standard form

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

Factor

- 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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

\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

5 \cdot \frac{π}{180}

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

R = 7 (0) - 11

What is (m-1)^3-2m(m^2-4)<1 ?
The solution to (m-1)^3-2m(m^2-4)<1 is (-5-sqrt(29))/2 <m<(sqrt(29)-5)/2 \lor m>2