query: $\sqrt{x + \sqrt {x + \sqrt{ x + \cdots } } } = 5$ then find the value of $x$.
positive_passages.docid: 686
positive_passages.text: $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
negative_passages.docid: 134176
negative_passages.text: For $x$ and $\lambda$ complex, if $|x| \gt \frac{1}{2} + \sqrt{\frac{5}{4} + |\lambda|}$ then $|x^2+\lambda| \gt |x| +1$
negative_passages.docid: 82591
negative_passages.text: Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
negative_passages.docid: 9490
negative_passages.text: Let $(1+x+x^2)^n=a_0+a_1x+a_2x^2+\cdots+a_{2n}x^{2n}$ be an identity in $x$. Find $a_0 +a_2 +a_4+ \cdots +a_{2n} $ in terms of $n$
negative_passages.docid: 133382
negative_passages.text: Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
negative_passages.docid: 121759
negative_passages.text: If this equation in x has real roots find the value of a and b.
negative_passages.docid: 39642
negative_passages.text: Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
negative_passages.docid: 49443
negative_passages.text: What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$?
negative_passages.docid: 116277
negative_passages.text: real values of $x$ in $\sqrt{5-x} = 5-x^2$.
negative_passages.docid: 11707
negative_passages.text: If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
negative_passages.docid: 11250
negative_passages.text: Evaluate the expression $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\cdots}}}$
negative_passages.docid: 59175
negative_passages.text: Given that $x+\frac{1}{x}=\sqrt{3}$, find $x^{18}+x^{24}$
negative_passages.docid: 8027
negative_passages.text: How to prove $\sqrt{x + y} \le \sqrt{x} + \sqrt{y}$?
negative_passages.docid: 149685
negative_passages.text: Formula for $\sqrt{a-\sqrt{a+\sqrt{a+\ldots}}}$
negative_passages.docid: 7
negative_passages.text: Find value of the limit: $\lim_{n\to \infty}\sqrt[n]{1^2+2^2+\cdots+n^2}$
negative_passages.docid: 51729
negative_passages.text: Solve the following equation: $\sqrt {\sin x - \sqrt {\cos x + \sin x} } = \cos x$
negative_passages.docid: 112171
negative_passages.text: Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.