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  • The numberof rational roots of 81(2x-5/3x+1)^4-45(2x-5/3x+1)^2+4=0, x is not equal to 13

The numberof rational roots of 81(2x-5/3x+1)^4-45(2x-5/3x+1)^2+4=0, x is not equal to 13

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Solution:   Put (2x-5/3x+1)^2=t,  so that equation becomes

                 81t^2-45t+4=0

           Rightarrow 81t^2-36t-9t+4=0 

          Rightarrow    (9t-1)(9t-4)=0

         Rightarrow    t=1/9,4/9Rightarrow (2x-5/3x+1)=pm 1/3,pm 2/3

        Thus , the given equation has four rational roots .

Posted by

Deependra Verma

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