AoPSWiki
Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
Personal tools

2007 Cyprus MO/Lyceum/Problem 1

From AoPSWiki

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\Longrightarrow\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
Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2007_Cyprus_MO/Lyceum/Problem_1"
Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us