query: Inequality with 4 variables in form of harmonized means
positive_passages.docid: 18119
positive_passages.text: Show that if a,b,c,d are positive then $\frac{ab}{a+b}+\frac{cd}{c+d}\le \frac{(a+c)(b+d)}{a+b+c+d}$
negative_passages.docid: 99820
negative_passages.text: symetric inequality for a rational function of three variables
negative_passages.docid: 128137
negative_passages.text: population and subsamples : mean equality?
negative_passages.docid: 74315
negative_passages.text: Constraint on variables in summation
negative_passages.docid: 119417
negative_passages.text: Tetrahedron inequality
negative_passages.docid: 106979
negative_passages.text: Prove the inequality and limitation
negative_passages.docid: 116685
negative_passages.text: Reciprocal of Holder's inequality
negative_passages.docid: 122156
negative_passages.text: An inequality concerning three positive numbers
negative_passages.docid: 71497
negative_passages.text: An inequality from Littlewood's Miscellany
negative_passages.docid: 44823
negative_passages.text: Prove the general arithmetic-geometric mean inequality
negative_passages.docid: 143801
negative_passages.text: Proving the AGM inequality with 3 variables
negative_passages.docid: 72961
negative_passages.text: Solving Inequalities with Gamma Function
negative_passages.docid: 151148
negative_passages.text: How to solve simultaneous inequalities?
negative_passages.docid: 45918
negative_passages.text: Inequality: $x^2+y^2+xy\ge 0$
negative_passages.docid: 126032
negative_passages.text: Proving a certain inequality
negative_passages.docid: 62578
negative_passages.text: Using AM-GM inequality
negative_passages.docid: 106373
negative_passages.text: Hölder's inequality with three functions