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Find t s.t. system of equations have solution - ILL1990 HUN2

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September 18, 2010
quadraticsinequalitiesalgebrasystem of equationsalgebra proposed

Problem Statement

Find the real number tt, such that the following system of equations has a unique real solution (x,y,z,v)(x, y, z, v):
{x+y+z+v=0(xy+yz+zv)+t(xz+xv+yv)=0 \left\{\begin{array}{cc}x+y+z+v=0\\ (xy + yz +zv)+t(xz+xv+yv)=0\end{array}\right.
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