Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 2"
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==Problem== | ==Problem== | ||
| − | The operation <math>\alpha * \beta</math> is defined by <math>\alpha * \beta = \alpha^2 - \beta^2 | + | The operation <math>\alpha*\beta</math> is defined by <math>\alpha*\beta=\alpha^2-\beta^2\ \forall\alpha,\beta\in\mathbb{R}</math>. |
| − | The value of the expression <math>K = \left[\left(1+\sqrt{3}\right) * 2\right]*\sqrt{2} </math> is | + | The value of the expression <math>K=\left[\left(1+\sqrt{3}\right)*2\right]*\sqrt{2}</math> is |
| − | + | <math>\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ 0\qquad\mathrm{(C)}\ \sqrt{3}\qquad\mathrm{(D)}\ 9\qquad\mathrm{(E)}\ 1</math> | |
| − | |||
| − | B | ||
| − | |||
| − | C | ||
| − | |||
| − | D | ||
| − | |||
| − | E | ||
==Solution== | ==Solution== | ||
| − | <math> | + | <math>(1+\sqrt{3})*2=(1+\sqrt{3})^2-2^2=1^2+2\sqrt{3}+3-4=2\sqrt{3}</math> |
| − | + | <math>2\sqrt{3}*\sqrt{2} = 12-2=10</math> | |
==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}} | ||
Latest revision as of 09:56, 27 April 2008
Problem
The operation 
is defined by 
.
The value of the expression ![$K=\left[\left(1+\sqrt{3}\right)*2\right]*\sqrt{2}$](http://latex.artofproblemsolving.com/c/8/d/c8d5601243c954d4130828021cd2ccb268de402e.png)
is
Solution
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 | ||
