Difference between revisions of "2007 Cyprus MO/Lyceum/Problem 1"
m (→Solution: so -> png) |
(→Solution) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 5: | Line 5: | ||
==Solution== | ==Solution== | ||
| − | <math>x^2 | + | 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}} | |
| − | |||
| − | |||
Latest revision as of 17:04, 17 March 2013
Problem
If 
, then the value of the expression 
is
Solution
Rearranging the variables in the equation gives, 
. Factoring the equation gives us 
. We are given that , therefore we can simplify the equation into 
, 
.
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 | ||
