Art of Problem Solving

AoPS Online

2007 Cyprus MO/Lyceum/Problem 1

Revision as of 16:15, 6 May 2007 by Azjps (talk | contribs) (→‎See also: trying new template)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 "https://artofproblemsolving.com/wiki/index.php?title=2007_Cyprus_MO/Lyceum/Problem_1&oldid=14963"

© 2024 AoPS Incorporated