# Questions tagged [inequalities]

Questions about handling with inequalities with, e.g., Reduce, Solve, FindInstance etc., their application in defining Regions, and ways to incorporate them into other computations, e.g. integration.

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### How can I find the domain of $x$ for which the function $g(x)\geq0\;$?

I have this function ($x>0$) $$f (x)=\frac{\sqrt{g (x)}+4 x \left(x^2+1\right) \sin (\pi x) \cos ((3+\pi ) x)}{x^4+2 x^2+1+\left(4 x^2+\left(x^2-1\right)^2 \cos (2 \pi x)\right)}$$ ...
129 views

### Validating an inequality

I want to show That: $$1+a^{2017}+b^{2017} \geq a^{10}b^7+a^7b^{2000}+a^{2000}b^{10} \\ a,b\in \mathbb{R}^+_0$$ I used Simplify and then Resolve That is taking forever: ...
496 views

### How do I find complex values that satisfy multiple inequalities?

I want to find $a,b \in \mathbb{C}$ such that $$|1-2a-2b| < 1 \quad \text{&} \quad |1-2a+2b| < 1$$ using mathematica. I tried to use ...
41 views

### How to use conditions with Reduce? [closed]

I am solving a simple inequality with Reduce: Reduce[r^2-d^2>0,d] I get a correct solution, but I would like to impose the ...
158 views

### Fast way to check if $f(x)>x$ for what value of $x$

In order to find the value $x$ for which $f(x)>x$, I tried it using the following code: ParallelTable[If[TrueQ[f[x]>x],x,Nothing],{x,0,10^9}] For some ...
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### Reduce function returns error

I am trying to prove the inequality below for the given condition stated, but I get a warning result. ...
66 views

### Reduce inequality does not finish

I am trying to show general cases of symmetry of regions. However, for the following, Reduce does not finish: ...
32 views

### Isolate variable in inequality

I'm having the most stupid of problems. Suppose I have a simple inequality like $$|2-x|>2.$$ The solution to this is $$x<0 , \,x>4.$$ This is pretty obvious, though Mathematica insists on ...
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### Getting values of 2 variables and a constant based on a single equation using a 3D graph

This is my function. ...