Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 2"

Revision as of 22:12, 17 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

$K=((\sqrt{3}+1)^2-2^2)^2-(\sqrt{2})^2=(3+2\sqrt{3}+1-4)^2-(\sqrt{2})^2=10$

I'm not gonna go to sleep until someone fixes that.

@@ 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>
+I'm not gonna go to sleep until someone fixes that.
 ==See also==
 {{CYMO box|year=2006|l=Lyceum|num-b=1|num-a=3}}

2006 Cyprus MO, Lyceum (Problems)
Preceded by Problem 1	Followed by Problem 3
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Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 2"

Revision as of 22:12, 17 October 2007

Problem

Solution

See also