Difference between revisions of "2007 Cyprus MO/Lyceum/Problem 1"

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(Solution)
 
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==Solution==
 
==Solution==
<math>x^2+x-2xy+y^2-y=x^2-2xy+y^2+x-y=(x-y)^2+x-y=(1)^2+1=2\Longrightarrow\mathrm{ A}</math>
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Rearranging the variables in the equation gives, <math>x^2-2xy+y^2+x-y</math>. Factoring the equation gives us <math>(x-y)^2+(x-y)</math>. We are given that <math>x-y=1</math>, therefore we can simplify the equation into <math>(1)^2+1=2</math>, <math>\boxed{\mathrm{A}}</math>.
  
 
==See also==
 
==See also==
 
{{CYMO box|year=2007|l=Lyceum|before=First Question|num-a=2}}
 
{{CYMO box|year=2007|l=Lyceum|before=First Question|num-a=2}}

Latest revision as of 16:04, 17 March 2013

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 $(1)^2+1=2$, $\boxed{\mathrm{A}}$.

See also

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