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Grade 12th PassOrganic Chemistry

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

Profile image of pankaj gupta
14 Years agoGrade 12th Pass
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1 Answer

Profile image of Ashwin Muralidharan IIT Madras
14 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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