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32

Part of 2000 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 2000 P-32 (Algebra)

Source:

7/8/2012
Find the sum of all possible values of f(2)f(2) such that f(x)f(y)−f(xy)=yx+xyf(x)f(y)-f(xy) = \frac{y}{x}+\frac{x}{y}, for every positive real numbers x,yx,y
<spanclass=′latex−bold′>(A)</span> 52<spanclass=′latex−bold′>(B)</span> −54<spanclass=′latex−bold′>(C)</span> 54<spanclass=′latex−bold′>(D)</span> 32<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ \frac{5}{2} \qquad<span class='latex-bold'>(B)</span>\ -\frac{5}{4} \qquad<span class='latex-bold'>(C)</span>\ \frac{5}{4} \qquad<span class='latex-bold'>(D)</span>\ \frac{3}{2} \qquad<span class='latex-bold'>(E)</span>\ \text{None}