query: Inequality involing square-root
positive_passages.docid: 12020
positive_passages.text: Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
negative_passages.docid: 118613
negative_passages.text: Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
negative_passages.docid: 126632
negative_passages.text: Proving Inequalities with Absolute values
negative_passages.docid: 131596
negative_passages.text: Symmetric Inequality in $\mathbb{R}$
negative_passages.docid: 61939
negative_passages.text: Induction of inequality involving AP
negative_passages.docid: 134049
negative_passages.text: Showing an inequality is valid
negative_passages.docid: 77026
negative_passages.text: Proof with inequalities
negative_passages.docid: 91131
negative_passages.text: Question regarding an inequality
negative_passages.docid: 91617
negative_passages.text: Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
negative_passages.docid: 12781
negative_passages.text: Prove the following inequality $\sqrt[n]{x_1x_2...x_n}\ge (n-1)$
negative_passages.docid: 120390
negative_passages.text: An inequality involving 4 real or complex numbers
negative_passages.docid: 66261
negative_passages.text: Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
negative_passages.docid: 32963
negative_passages.text: proving the inequality $\triangle\leq \frac{1}{4}\sqrt{(a+b+c)\cdot abc}$
negative_passages.docid: 137791
negative_passages.text: Proving inequality $\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq \sqrt{3 \left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)}$
negative_passages.docid: 49750
negative_passages.text: Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
negative_passages.docid: 3955
negative_passages.text: Square roots -- positive and negative
negative_passages.docid: 107601
negative_passages.text: Use of inequality $1 - \cos (x) \leq x^2 /2$