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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
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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