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Let [x] denote the greatest integer not exceeding the real number x , and alpha , beta and gamma are the roots of the equation x^3-3x^2-2x+1=0 , then [alpha ]+[beta ]+[gama] equals

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Solution:      By Bolzano's Location Theorem ,

                        f(-1)< 0,f(0)> 0

           Rightarrow        f(1)< 0,f(2)< 0,f(3)< 0,f(4)> 0.

           Rightarrow    -1< alpha < 0;0< eta < 1   and   3< gamma < 4.

            	herefore        [alpha]+[eta]+[gamma]=-1+0+3=2.

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Deependra Verma

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