What is x^4(1-x^2)+(x^3-5x^4)(x^3+5x^4)<0 ?

The solution to x^4(1-x^2)+(x^3-5x^4)(x^3+5x^4) 1/(sqrt(5))

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x^4(1-x^2)+(x^3-5x^4)(x^3+5x^4)<0

x^{4} (1 - x^{2}) + (x^{3} - 5 x^{4}) (x^{3} + 5 x^{4}) < 0

x < - \frac{1}{5} or x > \frac{1}{5}

Interval Notation

(- \infty, - \frac{1}{5}) \cup (\frac{1}{5}, \infty)

Decimal Notation

x < - 0.4472135955 or x > 0.4472135955

Solution steps

x^{4} (1 - x^{2}) + (x^{3} - 5 x^{4}) (x^{3} + 5 x^{4}) < 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < - \frac{1}{5} or x > \frac{1}{5}

\frac{x - 5}{( x ^{2} + x + 5 ) ( x ^{2} - 4 x - 5 )} > 0

(x - 1) (4 - x) \cdot (x - 5)^{2} < 0

(2 x + 1) \cdot e^{4} x < 0

x^{4} - 4 x^{2} < 0

(x + 4)^{20} < 0

What is x^4(1-x^2)+(x^3-5x^4)(x^3+5x^4)<0 ?
The solution to x^4(1-x^2)+(x^3-5x^4)(x^3+5x^4)<0 is x<-1/(sqrt(5))\lor x> 1/(sqrt(5))