2007 Cyprus MO/Lyceum/Problem 1

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

Rearranging the variables in the equation gives, $x^2-2xy+y^2+x-y$ . Factoring the equation gives us $(x-y)^2+(x-y)$ . We are given that $x-y=1$ , therefore we can simplify the equation into $(1)^2+1=2$ , $\boxed{\mathrm{A}}$ .

2007 Cyprus MO, Lyceum (Problems)
Preceded by First Question	Followed by Problem 2
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2007 Cyprus MO/Lyceum/Problem 1

Problem

Solution

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