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PolynomialAndEquation
PolynomialAndEquation
2015
Problem - 2171
Let $x, y$ and $z$ be real numbers such that $$ \begin{array}{rl} x^2 +2(y-1)(z-1) &=12 \\ y^2 +2(z-1)(x-1) &=6 \\ z^2 +2(x-1)(y-1) &=9 \end{array} $$ Find all the possible values of $x+y+z$.
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