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If \( \alpha, \beta ; \beta, \gamma \) and \( \gamma, \alpha \) are the roots of \( a_{i} x^{2}+b_{i} x+c_{i}=0 ; i=1,2,3 \) then show that
\( \mathrm{P} \)
\[
(\alpha+\beta+\gamma)+(\alpha \beta+\beta \gamma+\alpha \gamma)+\alpha \beta \gamma=\pm\left\{\prod_{i=1}^{3}\left(\frac{a_{i}-b_{i}+c_{i}}{a_{i}}\right)\right\}^{1 / 2}-1
\]
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