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  • The number of real solutions of the equation (27)^1/x +(12)^1/x=2(8^1/x) is

The number of real solutions of the equation (27)^1/x +(12)^1/x=2(8^1/x) is

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Solution:  We have ,   (27)^1/x +(12)^1/x=2(8)^1/x

             Rightarrow      (27/8)^1/x+(12/8)^1/x=2

             Rightarrow       (3/2)^3/x+(3/2)^1/x=2

          As         3/2> 1,(3/2)^t> 1,ifhspace0.2cmt> 0

           and      (3/2)^t< 1,ifhspace0.2cmt< 0.

          Thus ,      (3/2)^3/x+(3/2)^1/x< 2hspace0.2cmif hspace0.2cmx< 0

           and        (3/2)^3/x+(3/2)^1/x> 2hspace0.2cmif hspace0.2cmx> 0.

             Therefore it is possible if 1/x=0  

              But this is not true any real value of x. 

 

Posted by

Deependra Verma

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