MathDB
P28 [Algebra] - Turkish NMO 1st Round - 2003

Source:

May 18, 2014

Problem Statement

Let aa, xx, yy, zz be real numbers such that axy+z=3a1ax-y+z=3a-1 ve xay+z=a21x-ay+z=a^2-1, which of the followings cannot be equal to x2+y2+z2x^2+y^2+z^2?
<spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 43<spanclass=latexbold>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ \sqrt 2 \qquad<span class='latex-bold'>(B)</span>\ \sqrt 3 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ \sqrt[3]{4} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}