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

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

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

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

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2006 Cyprus MO, Lyceum (Problems)
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2006 Cyprus MO/Lyceum/Problem 2

Problem

Solution

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