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Omni-MATH / Define x star y=frac{sqrt{x^{2}+3 x y+y^{2}-2 x-2 y+4}}{x y+4}. Compute ((cdots((2007 star 2006) star 2005) star cdots) star 1)

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Define $x \star y=\frac{\sqrt{x^{2}+3 x y+y^{2}-2 x-2 y+4}}{x y+4}$. Compute $$((\cdots((2007 \star 2006) \star 2005) \star \cdots) \star 1)$$
Plain-text mathematical notation (without MathML)
Define $x \star y=\frac{\sqrt{x^{2}+3 x y+y^{2}-2 x-2 y+4}}{x y+4}$. Compute $$((\cdots((2007 \star 2006) \star 2005) \star \cdots) \star 1)$$
Original LaTeX notation
Define $x \star y=\frac{\sqrt{x^{2}+3 x y+y^{2}-2 x-2 y+4}}{x y+4}$. Compute $$((\cdots((2007 \star 2006) \star 2005) \star \cdots) \star 1)$$

Discussion

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Source and history

task_id
4c637d17-e1e8-506e-9740-4db85386952f
task_key
test--4c637d17-e1e8-506e-9740-4db85386952f
task_revision_id
1
config / split
/ test

Official source

initial import