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Find the number of real solutions of the equation Please mention by which number we have to divide 27 1/x + 12 1/x = 2.8 1/x


Find the number of real solutions of the equation


Please mention by which number we have to divide


 


271/x + 121/x =  2.81/x


Grade:12th Pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Pankaj,

 

Let 21/x = a

and 31/x = b.

 

Clearly a>0 and b>0 and a≠b.

 

The eqn becomes b3 + a2b = 2a3

Or a3-b3 + a3-a2b = 0

ie (a-b)(a2+b2+ab) + a2(a-b) = 0

ie (a-b)(2a2+b2+ab) = 0 -----------(1)

 

Clearly a≠b So a-b can never be 0, and 2a2+b2+ab > 0 {as a>0 and b>0)

 

And hence (1) will have no solution.

So the given equation can never be true for any value of x. And hence no solution.

 

Hope that helps.

 

All the best.

Regards,

Ashwin (IIT Madras).

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