query: An elementary algebraic inequality
positive_passages.docid: 145152
positive_passages.text: How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
negative_passages.docid: 13228
negative_passages.text: Proofs of AM-GM inequality
negative_passages.docid: 78144
negative_passages.text: How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?
negative_passages.docid: 53123
negative_passages.text: Trying to derive a contradiction with this simple inequality,
negative_passages.docid: 48092
negative_passages.text: Inequality involving a finite sum
negative_passages.docid: 115464
negative_passages.text: Inequality involving inner product and norm
negative_passages.docid: 90796
negative_passages.text: Inequality Regarding e
negative_passages.docid: 102464
negative_passages.text: Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
negative_passages.docid: 136290
negative_passages.text: a mathematical problem on inequalities
negative_passages.docid: 138195
negative_passages.text: An inequality for arctan$x$
negative_passages.docid: 138490
negative_passages.text: An inequality with a weird condition
negative_passages.docid: 61939
negative_passages.text: Induction of inequality involving AP
negative_passages.docid: 45918
negative_passages.text: Inequality: $x^2+y^2+xy\ge 0$
negative_passages.docid: 91617
negative_passages.text: Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
negative_passages.docid: 139692
negative_passages.text: Proof of inequality using AM-GM inequality
negative_passages.docid: 137507
negative_passages.text: triangular series and inequality
negative_passages.docid: 106979
negative_passages.text: Prove the inequality and limitation