query: Inequality question .
positive_passages.docid: 157068
positive_passages.text: Prove that $\left (\frac{1}{a}+1 \right)\left (\frac{1}{b}+1 \right)\left (\frac{1}{c}+1 \right) \geq 64.$
negative_passages.docid: 108782
negative_passages.text: Inequality $\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1} \ge 1$
negative_passages.docid: 156555
negative_passages.text: Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
negative_passages.docid: 138490
negative_passages.text: An inequality with a weird condition
negative_passages.docid: 45918
negative_passages.text: Inequality: $x^2+y^2+xy\ge 0$
negative_passages.docid: 25203
negative_passages.text: with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
negative_passages.docid: 78528
negative_passages.text: Trigonometric fraction Inequality question
negative_passages.docid: 110798
negative_passages.text: Problem using the AM-GM inequality
negative_passages.docid: 79491
negative_passages.text: Inequality $(a+b)^2 + (a+b+4c)^2\ge \frac{kabc}{a+b+c}$ for $a,b,c \in\mathbb{R}$
negative_passages.docid: 151148
negative_passages.text: How to solve simultaneous inequalities?
negative_passages.docid: 120390
negative_passages.text: An inequality involving 4 real or complex numbers
negative_passages.docid: 145089
negative_passages.text: Inequality: $7a+5b+12ab\le9$
negative_passages.docid: 85614
negative_passages.text: Do inequalities hold under differentiation?
negative_passages.docid: 53123
negative_passages.text: Trying to derive a contradiction with this simple inequality,
negative_passages.docid: 107967
negative_passages.text: Significance of assumption in competition inequality questions
negative_passages.docid: 99644
negative_passages.text: Finding an Upper Bound on This Inequality
negative_passages.docid: 126032
negative_passages.text: Proving a certain inequality