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If $\alpha, \beta,\gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a= \alpha ^2+\beta^2+\gamma^2, \;b= \alpha \beta + \beta \gamma+ \gamma \alpha$ and $ c= (\alpha+\beta)(\beta+\gamma)(\gamma+\alpha),$ then the correct inequality among the following is :

\[\begin {array} {1 1} (1)\;a < b < c & \quad (2)\;b < a < c \\ (3)\;b < c < a & \quad (4)\;c < a < b \end {array}\]

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(2) b < a <  c
answered Nov 7, 2013 by pady_1
edited Jan 2, 2014 by meena.p

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