What is sqrt(x^3-x)>0 ?

The solution to sqrt(x^3-x)>0 is -1 1

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sqrt(x^3-x)>0

x^{3} - x > 0

- 1 < x < 0 or x > 1

Interval Notation

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

Solution steps

x^{3} - x > 0

Square both sides

(x^{3} - x)^{2} > 0^{2}

Simplify

x^{3} - x > 0

x^{3} - x > 0 : - 1 < x < 0 or x > 1

- 1 < x < 0 or x > 1

Find singularity points

Find non-negative values for radicals:

- 1 \leq x \leq 0 or x \geq 1

Combine the intervals

(- 1 < x < 0 or x > 1) and (- 1 \leq x \leq 0 or x \geq 1)

Merge Overlapping Intervals

- 1 < x < 0 or x > 1

x + 8 = 14

∣ y - 5 ∣ < 3

x^{5} y^{4} + y^{2}

5 (x - 2) - 7 (x + 1) \leq - 4 x + 3

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