Difference between revisions of "1989 USAMO Problems/Problem 5"

Revision as of 15:41, 16 October 2007

Let $u$ and $v$ be real numbers such that

$(u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8.$

Determine, with proof, which of the two numbers, $u$ or $v$ , is larger.

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Revision as of 15:41, 16 October 2007 (view source) 1=2 (talk \| contribs) (New page: ==Problem== Let <math>u</math> and <math>v</math> be real numbers such that <math> (u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8. </math> Det...)		Revision as of 15:41, 16 October 2007 (view source) 1=2 (talk \| contribs) (→‎See Also) Newer edit →
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	==See Also==		==See Also==
		+	{{USAMO box\|year=1989\|num-b=4\|after=Final Question}}

1989 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Final Question
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions