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  • If both roots of the equation x^2-2ax+a^2-1=0 lie between -3 and 4 , then [a] cannot be ( where [.] denote the greatest integer function)

If both roots of the equation x^2-2ax+a^2-1=0 lie between -3 and 4 , then [a] cannot be ( where [.] denote the greatest integer function)

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Solution:  The equation is  x^2-2ax+a^2-1=0

        \ \ Rightarrow hspace1cm (x-a)^2=1\ \ Rightarrow hspace1cmx=apm1Rightarrow a-1< a+1\ \ Rightarrow hspace1cma-1> -3 hspace0.5cmand hspace0.5cma+1< 4\ \ Rightarrow hspace1cma> -2 hspace0.5cm,a< 3\ \ Rightarrow hspace1cm-2< a< 3 herefore [a]=-2,-1,0,1,2

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Deependra Verma

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