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2007 Cyprus MO/Lyceum/Problem 1

Revision as of 11:20, 6 May 2007 by I_like_pie (talk | contribs)
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Problem

If $x-y=1$, then the value of the expression $K=x^2+x-2xy+y^2-y$ is

$\mathrm{(A) \ } 2\qquad \mathrm{(B) \ } -2\qquad \mathrm{(C) \ } 1\qquad \mathrm{(D) \ } -1\qquad \mathrm{(E) \ } 0$

Solution

$x^2+x-2xy+y^2-y=x^2-2xy+y^2+x-y=(x-y)^2+x-y=(1)^2+1=2\Rightarrow\mathrm{ A}$

See also

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