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If a,b respectively be the number of solutions and sum of solutions of |2x/x-1| - |x| = x^2/|x-1| then a and b equal to ?

If a,b respectively be the number of solutions and sum of solutions of |2x/x-1|  - |x| = x^2/|x-1| then a and b equal to ?
 
 

Grade:12

1 Answers

Hemanth Hemanth
16 Points
4 years ago
(2x/|x-1| ) - |x| = (x2 /|x-1| )
If mod. is positive then |x-1| = x-1
Then, [2x/(x-1)] - x = x2 / (x-1)
Then on solving the quadratic equation in (x), we get the values of (x) as x = 0, 3/2.
If mod. is negative then |x-1| = 1-×
Then [2x/(1-x)] - (-x) = [x2/(1-x)]
Hendon solving the quadratic equation we get the values of (x) as 0,3/2.
Hence only two value of ( x) satisfy the condition.
Therefore, a =2  and b=0+3/2 = 3/2.

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