0

Solve this inequality

In[41]:= Reduce[x^2 > x^(1/3), x, Reals]

Out[41]= x > 1

Missing a solution as

x<0

There was also an error in drawing images of two functions within the same coordinate system

Plot[{x^2, x^(1/3)}, {x, -3, 3}, AspectRatio -> 1, 
 PlotLabels -> Automatic, Axes -> True, 
 AxesStyle -> Arrowheads[{0.0, 0.04}], AxesLabel -> {x, y}, 
 ImageSize -> Medium, PlotHighlighting -> "XSlice"]

enter image description here

The correct image is

enter image description here

In[45]:= FunctionDomain[x^(1/3), x]

Out[45]= x >= 0

The Domain of a function of this function is also wrong

xzczd
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csn899
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1 Answers1

6

In Mathematica, x^(1/3)===Power[x,1/3] is a complex function which is difference from the real cube root of x.

we should use

Reduce[x^2 > CubeRoot[x], x, Reals]

x < 0 || x > 1.

or

Reduce[x^2 > Root[#^3 - x &, 1], x, Reals]

x < 0 || x > 1.

Plot[{x^2, Root[#^3 - x &, 1]}, {x, -2, 2}, AspectRatio -> Automatic]

enter image description here

cvgmt
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