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Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 2"
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==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 19:17, 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
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