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2007 iTest Problems/Problem 48

Revision as of 22:02, 7 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Let a and b be relatively prime positive integers such that <math>a/b</math> is the maximum possible value of <math>\sin^2x_1+\sin^2x_2+\sin^2x_3+\cdots+\sin^2x_{2...")
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Problem

Let a and b be relatively prime positive integers such that $a/b$ is the maximum possible value of $\sin^2x_1+\sin^2x_2+\sin^2x_3+\cdots+\sin^2x_{2007}$, where, for $1\leq i\leq 2007, x_i$ is a nonnegative real number, and $x_1+x_2+x_3+\cdots+x_{2007}=\pi$. Find the value of $a+b$.

Solution

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