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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.

2 votes
1 answer
110 views

Solving a coupled system of inequalities over integers

! tried to solve $ \frac{999999}{1000000}<a+\sqrt{2} b\land a+\sqrt{2} b<1$ over the integers through Reduce[999999/1000000 < a + Sqrt[2]* b && a + Sqrt[2]*b < 1, {a,b}, Integers] *(a|b)∈ Integers&&( …
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4 votes
1 answer
617 views

How to solve a conditional inequality?

I am trying to use Mathematica to solve a conditional inequality. Find all (real) numbers $a$ and $b$ such that $|a| + |b| \ge 2/ \sqrt{3}$ and for any real $x$ the inequality $ |a\sin x + b \sin …
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2 votes
3 answers
278 views

How to prove or disprove an inequality with Mathematica?

I mean there exist $\lambda>0, x\in \mathbb R$ s.t. the inequality $$ \frac{3^{\lambda } e^x+e^{3 x}+1}{2^{\lambda } e^{2 x}}<\frac{1}{10^{100}}$$ is valid. Here are my unsuccessful attempts. Resolve[ …
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