If \( \mathrm{a}, \mathrm{b} \) and \( \mathrm{c} \) are distinct r...

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If \( \mathrm{a}, \mathrm{b} \) and \( \mathrm{c} \) are distinct real numbers, such that the
\( \mathrm{P} \) quadratic expressions \( Q_{1}(x)=a x^{2}+b x+c, Q_{2}(x)= \)

W \( b x^{2}+c x+a \) and \( Q_{3}(x)=c x^{2}+a x+b \) are always non-negative, then find the number of possible integers in the range of the expression \( y=\frac{a^{2}+b^{2}+c^{2}}{a b+b c+c a} \)
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