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

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==Solution==
 
==Solution==
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<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==
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{{CYMO box|year=2007|l=Lyceum|before=First question|num-a=2}}
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{{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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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