query: inequality between 3 square roots
positive_passages.docid: 28499
positive_passages.text: Inequality.$\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq 3$
negative_passages.docid: 111903
negative_passages.text: An inequality for sides of a triangle
negative_passages.docid: 139177
negative_passages.text: Ramsey Number Inequality: $R(\underbrace{3,3,...,3,3}_{k+1}) \le (k+1)(R(\underbrace{3,3,...3}_k)-1)+2$
negative_passages.docid: 21457
negative_passages.text: Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
negative_passages.docid: 106373
negative_passages.text: Hölder's inequality with three functions
negative_passages.docid: 118244
negative_passages.text: An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
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: 91871
negative_passages.text: Proving quadratic inequalities?
negative_passages.docid: 141525
negative_passages.text: Cyclic Inequality $\frac{a^3}{(a+b)(a+c)}$
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality
negative_passages.docid: 27796
negative_passages.text: inequality of absolute value problem
negative_passages.docid: 104922
negative_passages.text: Inequality $\frac1a + \frac1b + \frac1c \leq \frac{a^8+b^8+c^8}{a^3b^3c^3}$
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: 7966
negative_passages.text: How prove $ \sqrt{2}+\sqrt{3}>\pi$?
negative_passages.docid: 134764
negative_passages.text: Triangle Inequality question with fractions
negative_passages.docid: 144244
negative_passages.text: Bound on difference between irrational square root and rational number
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$