query: Proving the AM-GM inequality for 3 variables
positive_passages.docid: 143801
positive_passages.text: Proving the AGM inequality with 3 variables
negative_passages.docid: 153538
negative_passages.text: Proving Holder's inequality using Jensen's inequality
negative_passages.docid: 23119
negative_passages.text: An application of Jensen's Inequality
negative_passages.docid: 131543
negative_passages.text: inequality with three variables and condition
negative_passages.docid: 152311
negative_passages.text: Proving expression$\geq 2$, where variables are $x,y,z$
negative_passages.docid: 117281
negative_passages.text: How prove this inequality $x^3y+y^3z+z^3x\ge xyz(x+y+z)$
negative_passages.docid: 119417
negative_passages.text: Tetrahedron inequality
negative_passages.docid: 88605
negative_passages.text: Proof of the Reverse Triangle Inequality
negative_passages.docid: 52618
negative_passages.text: AM-GM inequality basic
negative_passages.docid: 15116
negative_passages.text: Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$
negative_passages.docid: 27954
negative_passages.text: Prove triangle inequality using the properties of absolute value
negative_passages.docid: 106373
negative_passages.text: Hölder's inequality with three functions
negative_passages.docid: 146656
negative_passages.text: Multivariate Application of Slutsky's lemma
negative_passages.docid: 14677
negative_passages.text: Proving the exponential inequality: $x^y+y^x\gt1$
negative_passages.docid: 77192
negative_passages.text: How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
negative_passages.docid: 6613
negative_passages.text: AM-GM inequality: $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{d} + \frac{d^2}{a} \geq a + b + c + d$
negative_passages.docid: 105268
negative_passages.text: prove inequality through mean value theorem