query: Find the value of $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ca}+\frac{c^2}{2c^2+ab}$
positive_passages.docid: 26287
positive_passages.text: Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$
negative_passages.docid: 98305
negative_passages.text: How do I show that $\sum_{cyc} \frac {a^6}{b^2 + c^2} \ge \frac {abc(a + b + c)}2?$
negative_passages.docid: 116649
negative_passages.text: Value of: $ \frac {1} {\sqrt {4} + \sqrt {5}} + \frac {1} {\sqrt {5} + \sqrt {6}} + ... + \frac {1} {\sqrt {80} + \sqrt {81}}$
negative_passages.docid: 76941
negative_passages.text: How do you find the value of $\sum_{r=0}^{44} \tan^2(2r+1)$?
negative_passages.docid: 133448
negative_passages.text: What is the value of $a/b/c$?
negative_passages.docid: 123475
negative_passages.text: $\frac{1}{A_1A_2}=\frac{1}{A_1A_3}+\frac{1}{A_1A_4}$.Then find the value of $n$
negative_passages.docid: 14763
negative_passages.text: How to prove $\frac{1}{4}(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a})\ge \sqrt[4]{\frac{a^4+b^4+c^4+d^4}{4}}$
negative_passages.docid: 74120
negative_passages.text: Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
negative_passages.docid: 94831
negative_passages.text: Finding value of $a +b+c$
negative_passages.docid: 105117
negative_passages.text: $1 + \frac{1}{3}\frac{1}{4} + \frac{1}{5}\frac{1}{4^2} + \frac{1}{7}\frac{1}{4^3} + ..........$
negative_passages.docid: 67034
negative_passages.text: Find the value of $\alpha + \beta + \alpha\beta$ from the given data
negative_passages.docid: 41619
negative_passages.text: How find the maximum value of $|bc|$
negative_passages.docid: 115719
negative_passages.text: Find the possible values of |A + B + C |
negative_passages.docid: 67666
negative_passages.text: show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$
negative_passages.docid: 137027
negative_passages.text: Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
negative_passages.docid: 111847
negative_passages.text: For $a,b,c>0$, prove that $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c+\frac{4(a-b)^2}{a+b+c}$
negative_passages.docid: 11868
negative_passages.text: Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$