query: Is there an arithmetic proof to the AM GM Inequality for 3 variables?
positive_passages.docid: 28218
positive_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 56166
negative_passages.text: Prove that $\frac{a}{b+2c+3d}+\frac{b}{c+2d+3a}+\frac{c}{d+2a+3b}+\frac{d}{a+2b+3c} \geq \frac{2}{3}.$
negative_passages.docid: 131543
negative_passages.text: inequality with three variables and condition
negative_passages.docid: 58969
negative_passages.text: A proof for the inequality $\sum_{i=0}^{t-2}{\frac{1}{t+3i}} \leq \frac{1}{2} $ for all $t \geq 2$
negative_passages.docid: 93599
negative_passages.text: General Proof for the triangle inequality
negative_passages.docid: 96133
negative_passages.text: Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $.
negative_passages.docid: 112676
negative_passages.text: Inequality $(a+b+c)(ab+bc+ca)(a^3+b^3+c^3)\le (a^2+b^2+c^2)^3$
negative_passages.docid: 105047
negative_passages.text: Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
negative_passages.docid: 117171
negative_passages.text: De-Morgan's theorem for 3 variables?
negative_passages.docid: 91871
negative_passages.text: Proving quadratic inequalities?
negative_passages.docid: 116781
negative_passages.text: Could someone give a detailed (yet elementary) proof for Jensen's inequality?
negative_passages.docid: 56101
negative_passages.text: Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$
negative_passages.docid: 77134
negative_passages.text: Proving a three variables inequality
negative_passages.docid: 74486
negative_passages.text: How to understand Cauchy's proof of AM-GM inequality(the last step)
negative_passages.docid: 119417
negative_passages.text: Tetrahedron inequality
negative_passages.docid: 157416
negative_passages.text: Prove inequality: $\sum \frac{a^4}{a^3+b^3} \ge \frac{a+b+c}{2}$
negative_passages.docid: 145152
negative_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 $(x,y,z)\in[1,2]^3$