What is sqrt(x^3)>= x ?

The solution to sqrt(x^3)>= x is x=0\lor x>= 1

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sqrt(x^3)>= x

x^{3} \geq x

x = 0 or x \geq 1

Interval Notation

x = 0 \cup [1, \infty)

Solution steps

x^{3} \geq x

f (x) \geq g (x)

then

g (x) < 0 or g (x) \geq 0

For

x < 0 : x < 0

For

x \geq 0 : x = 0 or x \geq 1

Find singularity points

Find non-negative values for radicals:

x \geq 0

Combine the intervals

(x = 0 or x \geq 1 or x < 0) and x \geq 0

Merge Overlapping Intervals

x = 0 or x \geq 1

Verify Solutions:

x = 0

True

, x \geq 1

True

The solution is

x = 0 or x \geq 1

\frac{n}{2} - 1 < 1

x^{2} - 2 x - 24 = 0

3 y^{2} + 11 y - 20

12 x^{2} + 8 x - 15 = 0

∣ 2 y - 3 ∣ \geq 12