query: Manipulating an inequality:
positive_passages.docid: 94119
positive_passages.text: Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
negative_passages.docid: 56391
negative_passages.text: Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
negative_passages.docid: 53112
negative_passages.text: Proving using AM-GM inequality
negative_passages.docid: 131596
negative_passages.text: Symmetric Inequality in $\mathbb{R}$
negative_passages.docid: 47644
negative_passages.text: Inequality involving rearrangement: $ \sum_{i=1}^n |x_i - y_{\sigma(i)}| \ge \sum_{i=1}^n |x_i - y_i|. $
negative_passages.docid: 62578
negative_passages.text: Using AM-GM inequality
negative_passages.docid: 143968
negative_passages.text: Proving this inequality by mathematical induction
negative_passages.docid: 77493
negative_passages.text: Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
negative_passages.docid: 144127
negative_passages.text: Inequality from Challenge and Thrill of Pre-college Mathematics
negative_passages.docid: 23264
negative_passages.text: Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality
negative_passages.docid: 85614
negative_passages.text: Do inequalities hold under differentiation?
negative_passages.docid: 30386
negative_passages.text: Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
negative_passages.docid: 14951
negative_passages.text: Other Idea to show an inequality $\dfrac{1}{\sqrt 1}+\dfrac{1}{\sqrt 2}+\dfrac{1}{\sqrt 3}+\cdots+\dfrac{1}{\sqrt n}\geq \sqrt n$
negative_passages.docid: 136290
negative_passages.text: a mathematical problem on inequalities
negative_passages.docid: 106373
negative_passages.text: Hölder's inequality with three functions
negative_passages.docid: 158276
negative_passages.text: Inequality problem involving square roots