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1987 AMC 12 #15 - Multiple Equations

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December 31, 2011
AMC

Problem Statement

If (x,y)(x, y) is a solution to the system xy=6andx2y+xy2+x+y=63, xy=6 \qquad \text{and} \qquad x^2y+xy^2+x+y=63, find x2+y2.x^2+y^2.
<spanclass=′latex−bold′>(A)</span> 13<spanclass=′latex−bold′>(B)</span> 117332<spanclass=′latex−bold′>(C)</span> 55<spanclass=′latex−bold′>(D)</span> 69<spanclass=′latex−bold′>(E)</span> 81 <span class='latex-bold'>(A)</span>\ 13 \qquad<span class='latex-bold'>(B)</span>\ \frac{1173}{32} \qquad<span class='latex-bold'>(C)</span>\ 55 \qquad<span class='latex-bold'>(D)</span>\ 69 \qquad<span class='latex-bold'>(E)</span>\ 81
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