Art of Problem Solving
Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2006 Cyprus MO/Lyceum/Problem 2: Difference between revisions

← Older editNewer edit →
1=2 (talk | contribs)
4,129 edits
No edit summary
No edit summary
Line 14: Line 14:


==Solution==
==Solution==
<math>K=((\sqrt{3}+1)^2-2^2)^2-(\sqrt{2})^2=(3+2\sqrt{3}+1-4)^2-(\sqrt{2})^2=10</math>
<math>(1+\sqrt{3}) * 2 =(1+\sqrt{3})^2-2^2=1^2+2\sqrt{3}+3-4=2\sqrt{3}</math>


I'm not gonna go to sleep until someone fixes that.
<math>2\sqrt{3} * \sqrt{2} = 12-2=10</math>
 
I think that B was mistyped, and that it is supposed to be 10.
 
{{wikify}}


==See also==
==See also==
{{CYMO box|year=2006|l=Lyceum|num-b=1|num-a=3}}
{{CYMO box|year=2006|l=Lyceum|num-b=1|num-a=3}}

Revision as of 18:17, 19 October 2007

Problem

The operation $\alpha * \beta$ is defined by $\alpha * \beta = \alpha^2 - \beta^2$ $\forall \alpha , \beta \in R$. The value of the expression $K = \left[\left(1+\sqrt{3}\right) * 2\right]*\sqrt{2}$ is

A. $3$

B. $0$

C. $\sqrt{3}$

D. $9$

E. $1$

Solution

$(1+\sqrt{3}) * 2 =(1+\sqrt{3})^2-2^2=1^2+2\sqrt{3}+3-4=2\sqrt{3}$

$2\sqrt{3} * \sqrt{2} = 12-2=10$

I think that B was mistyped, and that it is supposed to be 10.

Template:Wikify

See also

2006 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 1 		Followed by
Problem 3
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://wiki.aopstest.com/wiki/index.php?title=2006_Cyprus_MO/Lyceum/Problem_2&oldid=18380"