query: If $y =\sqrt{5+\sqrt{5-\sqrt{5+ \cdots}}}$, what is the value of $y^2-y$?
positive_passages.docid: 145595
positive_passages.text: $\text{Let }y=\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5-...}}}} $, what is the nearest value of $y^2 - y$?
negative_passages.docid: 113386
negative_passages.text: Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$
negative_passages.docid: 115213
negative_passages.text: How to simplify $\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}$
negative_passages.docid: 138931
negative_passages.text: Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
negative_passages.docid: 139755
negative_passages.text: Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
negative_passages.docid: 148968
negative_passages.text: Equation of conic: Given five points on it
negative_passages.docid: 107142
negative_passages.text: If $(x_n) \to x$ then $(\sqrt[n]{x_1x_2\cdots x_n}) \to x$
negative_passages.docid: 143409
negative_passages.text: Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.
negative_passages.docid: 144765
negative_passages.text: Solving $\sqrt{x+5} = x - 1$
negative_passages.docid: 78719
negative_passages.text: Solve the DE $yy^{\prime}+x=\sqrt{x^2+y^2}$
negative_passages.docid: 11707
negative_passages.text: If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$
negative_passages.docid: 49443
negative_passages.text: What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$?
negative_passages.docid: 31317
negative_passages.text: If we know $x+y+z=1$, $x^2+y^2+z^2=2$, and $x^3+y^3+z^3=3$, how to find $x^4+y^4+z^4$?
negative_passages.docid: 117392
negative_passages.text: Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
negative_passages.docid: 54576
negative_passages.text: If $ 5x+12y=60$ , what is the minimum of $\sqrt{x^2+y^2}$?
negative_passages.docid: 59818
negative_passages.text: Why $(-2)^{2.5}$ isn't equal to $((-2)^{25})^{1/10}$?
negative_passages.docid: 17102
negative_passages.text: If $\left(1+\sin \phi\right)\cdot \left(1+\cos \phi\right) = \frac{5}{4}\;,$ Then $\left(1-\sin \phi\right)\cdot \left(1-\cos \phi\right)$