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2007 Cyprus MO/Lyceum/Problem 4

Revision as of 12:45, 6 May 2007 by I_like_pie (talk | contribs)
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Problem

We define the operation $a*b = \frac{1+a}{1+b^2}$, $\forall a,b \in \real$.

The value of $(2*0)*1$ is

$\mathrm{(A) \ } 2\qquad \mathrm{(B) \ } 1\qquad \mathrm{(C) \ } 0\qquad \mathrm{(D) \ } \frac{1}{2}\qquad \mathrm{(E) \ } \frac{5}{2}$

Solution

$\frac{1+\frac{1+2}{1+0^2}}{1+1^2}=\frac{1+3}{2}=2\Rightarrow\mathrm{ A}$

See also

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