Algebra · Symmetric expressions · Absolute value · Sign analysis
Let \(x\), \(y\) and \(z\) be real numbers such that
\[ x^{2} + y^{2} + z^{2} = 18 \qquad \text{and} \qquad xy + yz + zx = 9 . \]
Determine the value of \(|x| + |y| + |z|\).
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Serbian Regional Competition 2005, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source