MathDB

35

Part of 2012 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 2012 Problem - 35 {Algebra}

Source:

7/1/2012
For every positive real pair (x,y)(x,y) satisfying the equation x3+y4=x2yx^3+y^4 = x^2y, if the greatest value of xx is AA, and the greatest value of yy is BB, then A/B=?A/B = ?
<spanclass=′latex−bold′>(A)</span> 23<spanclass=′latex−bold′>(B)</span> 512729<spanclass=′latex−bold′>(C)</span> 7291024<spanclass=′latex−bold′>(D)</span> 34<spanclass=′latex−bold′>(E)</span> 243256 <span class='latex-bold'>(A)</span>\ \frac{2}{3} \qquad <span class='latex-bold'>(B)</span>\ \frac{512}{729} \qquad <span class='latex-bold'>(C)</span>\ \frac{729}{1024} \qquad <span class='latex-bold'>(D)</span>\ \frac{3}{4} \qquad <span class='latex-bold'>(E)</span>\ \frac{243}{256}
inequalities