query: Prove an inequality for positive real numbers
positive_passages.docid: 152053
positive_passages.text: Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$
negative_passages.docid: 38448
negative_passages.text: Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
negative_passages.docid: 101792
negative_passages.text: By expanding $e^x$ into a series prove the following inequality
negative_passages.docid: 56818
negative_passages.text: Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
negative_passages.docid: 40936
negative_passages.text: How prove this integral inequality
negative_passages.docid: 149287
negative_passages.text: Prove that $A,B>0$ and $A_{ij}0$
negative_passages.docid: 13656
negative_passages.text: Prove existence of a real root.
negative_passages.docid: 45711
negative_passages.text: Inequality with complex numbers
negative_passages.docid: 140599
negative_passages.text: Inequality Proof in Real Numbers: If $p+q=1$ then $pq\le\frac14$
negative_passages.docid: 120309
negative_passages.text: Number Theory Inequality Proof
negative_passages.docid: 20863
negative_passages.text: how do I prove this inequallity?
negative_passages.docid: 27691
negative_passages.text: How to prove Boole’s inequality
negative_passages.docid: 5369
negative_passages.text: Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
negative_passages.docid: 122156
negative_passages.text: An inequality concerning three positive numbers
negative_passages.docid: 31544
negative_passages.text: How to prove that this polynomial is larger than another for positive reals?
negative_passages.docid: 45090
negative_passages.text: Given any positive real numbers $a,b,c$, we have $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
negative_passages.docid: 157328
negative_passages.text: A complex analysis problem to prove an inequality