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Beliebt Algebra >

4x(1-x^2)(x^2-5x+6)>0

Lösung

4 x (1 - x^{2}) (x^{2} - 5 x + 6) > 0

Lösung

x < - 1 or 0 < x < 1 or 2 < x < 3

+1

Intervall-Notation

(- \infty, - 1) \cup (0, 1) \cup (2, 3)

Schritte zur Lösung

4 x (1 - x^{2}) (x^{2} - 5 x + 6) > 0

Rewrite in standard form

- x^{5} + 5 x^{4} - 5 x^{3} - 5 x^{2} + 6 x > 0

Faktorisiere

- x^{5} + 5 x^{4} - 5 x^{3} - 5 x^{2} + 6 x : - x (x + 1) (x - 1) (x - 2) (x - 3)

- x (x + 1) (x - 1) (x - 2) (x - 3) > 0

Multipliziere beide Seiten mit

- 1

(drehe die Ungleichung um)

(- x (x + 1) (x - 1) (x - 2) (x - 3)) (- 1) < 0 \cdot (- 1)

Vereinfache

x (x + 1) (x - 1) (x - 2) (x - 3) < 0

Identifiziere die Intervalle

x < - 1 or 0 < x < 1 or 2 < x < 3

Graph

Beliebte Beispiele

3(x+2)^2-2(3x-1)^2-3x(x+4)>-38

3 (x + 2)^{2} - 2 (3 x - 1)^{2} - 3 x (x + 4) > - 38

((x+1))/((x-1))>= ((x+5))/((x+1))

\frac{( x + 1 )}{( x - 1 )} \geq \frac{( x + 5 )}{( x + 1 )}

-5((x+1)/5)(x-5)>0

- 5 (\frac{x + 1}{5}) (x - 5) > 0

(10x-7)(x-5)<= 0

(10 x - 7) (x - 5) \leq 0

- 3 x^{2} + 7 x + 6 > 0