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

Step-by-step solution

Given equation x^3-6 x^2+11 x-6=0 has the roots , . Given, a= ^2+ ^2+ ^2 ...(i) b= + + ...(ii) c=( + )( + )( + ) ...(iii) In cubic equation the sum of the roots + + =- ( -6 1 )=6 + + = ( 11 1 )=11 product of the roots =- ( -6 1 )=6 From Eq. (ii), b=11 From Eq. (i), a= ^2+ ^2+ ^2 a=( + + )^2-2( + + ) a=(6)^2-2(11) 36-22 a=14 From Eq. (iii) c=( + )( + )( + )= ( + ^2+ + )( + )= + ^2 + ^2+ ^2+ ^2 + ^2+ ^2 + c=[( + + )- ][( + + )- ][( + + )- ]=(6- )(6- )(6- )=(36-6 -6 + )(6- )=216-36 -36 +6 -36 +6 +6 - =216- +6( + + )-3