query: How to explain this inequality in a direct way?
positive_passages.docid: 5694
positive_passages.text: How to prove $a^2 + b^2 + c^2 \ge ab + bc + ca$?
negative_passages.docid: 25203
negative_passages.text: with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
negative_passages.docid: 30386
negative_passages.text: Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
negative_passages.docid: 44233
negative_passages.text: How to prove this inequality $ x + \frac{1}{x} \geq 2 $
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: 126632
negative_passages.text: Proving Inequalities with Absolute values
negative_passages.docid: 140299
negative_passages.text: Inequality based on triangle: $\frac{3}{2}\le\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$
negative_passages.docid: 38448
negative_passages.text: Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
negative_passages.docid: 66707
negative_passages.text: How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $
negative_passages.docid: 2504
negative_passages.text: Inequality $\left|\,x_1\,\right|+\left|\,x_2\,\right|+\cdots+\left|\,x_p\,\right|\leq\sqrt{p}\sqrt{x^2_1+x^2_2+\cdots+x^2_p}$
negative_passages.docid: 117262
negative_passages.text: Proving a logarithm inequality
negative_passages.docid: 23979
negative_passages.text: Inequality involving sides of a triangle
negative_passages.docid: 49909
negative_passages.text: Inequality with five variables
negative_passages.docid: 115335
negative_passages.text: How can we prove this integral inequality?
negative_passages.docid: 40936
negative_passages.text: How prove this integral inequality
negative_passages.docid: 90796
negative_passages.text: Inequality Regarding e
negative_passages.docid: 33543
negative_passages.text: is "y1 < x < y2" an inequality or inequalities?