What is x(1-x^2)^3>3(1-x^2)^3 ?

The solution to x(1-x^2)^3>3(1-x^2)^3 is x<-1\lor 1<x<3

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x(1-x^2)^3>3(1-x^2)^3

x (1 - x^{2})^{3} > 3 (1 - x^{2})^{3}

x < - 1 or 1 < x < 3

Interval Notation

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

Solution steps

x (1 - x^{2})^{3} > 3 (1 - x^{2})^{3}

Rewrite in standard form

x - 3 x^{3} + 3 x^{5} - x^{7} + 3 x^{6} - 9 x^{4} + 9 x^{2} - 3 > 0

Factor

x - 3 x^{3} + 3 x^{5} - x^{7} + 3 x^{6} - 9 x^{4} + 9 x^{2} - 3 : - (x + 1)^{3} (x - 1)^{3} (x - 3)

- (x + 1)^{3} (x - 1)^{3} (x - 3) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x + 1)^{3} (x - 1)^{3} (x - 3)) (- 1) < 0 \cdot (- 1)

Simplify

(x + 1)^{3} (x - 1)^{3} (x - 3) < 0

Identify the intervals

x < - 1 or 1 < x < 3

0 = x^{2} + x - 30

\frac{18}{25}

x^{2} + 5 x + 4 \geq 0

2 x - 3 < 1 + x < 3 x - 1

e^{- 0.1}

What is x(1-x^2)^3>3(1-x^2)^3 ?
The solution to x(1-x^2)^3>3(1-x^2)^3 is x<-1\lor 1<x<3