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[" QUADRATIC EQUATIONS "],[" 46."(1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)]

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Solvef or x,(1)/((x-1)(x-2))+(1)/((x-2)(x-3))+(1)/((x-3)(x-4))=(1)/(6)

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Let x_(1),x_(2), be the roots of the quadratic equation x^(2)+ax+b=0 and x_(3),x_(4), be the roots of the quadratic equation x^(2)-ax+b-2=0. If (1)/(x_(1))+(1)/(x_(2))+(1)/(x_(3))+(1)/(x_(4))=(5)/(6) and x_(1)x_(2)x_(3)x_(4)=24 then find the value of a .