Grade 12Algebra

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 ?

Ash

7 Years agoGrade 12

7 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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