query: Cyclic inequality with fractions
positive_passages.docid: 29342
positive_passages.text: Prove the inequality: $(y+z)*x^4+(x+z)*y^4+(x+y)*z^4\le((x+y+z)^5)/12$ for positive reals.
negative_passages.docid: 99644
negative_passages.text: Finding an Upper Bound on This Inequality
negative_passages.docid: 134535
negative_passages.text: Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
negative_passages.docid: 105047
negative_passages.text: Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
negative_passages.docid: 44233
negative_passages.text: How to prove this inequality $ x + \frac{1}{x} \geq 2 $
negative_passages.docid: 54905
negative_passages.text: A classical inequality involving the central binomial coefficient
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: 83386
negative_passages.text: Inequality with exponents $x^x+y^y \ge x^y +y^x$
negative_passages.docid: 8207
negative_passages.text: Can I prove this inequality algebraically?
negative_passages.docid: 97694
negative_passages.text: Simple Divisor Summation Inequality (with Moebius function)
negative_passages.docid: 66082
negative_passages.text: Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$
negative_passages.docid: 24925
negative_passages.text: Recurrence Inequality
negative_passages.docid: 52204
negative_passages.text: Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
negative_passages.docid: 85763
negative_passages.text: Inequality $(1+\frac1k)^k \leq 3$
negative_passages.docid: 4099
negative_passages.text: Inequality $\sum\limits_{cyc}\frac{a^3}{13a^2+5b^2}\geq\frac{a+b+c}{18}$
negative_passages.docid: 20816
negative_passages.text: Inequalities with assumptions and constraints
negative_passages.docid: 77026
negative_passages.text: Proof with inequalities