2006 Cyprus MO/Lyceum/Problem 2

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.

2006 Cyprus MO, Lyceum (Problems)
Preceded by Problem 1	Followed by Problem 3
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2006 Cyprus MO/Lyceum/Problem 2

Problem

Solution

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