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if the equation a/x-a + b/x-b = 1 has roots equal in magnitude but opposite in sign,then value of a+b is?

if the equation a/x-a + b/x-b = 1 has roots equal in magnitude but opposite in sign,then value of a+b is?

Grade:12

2 Answers

surendra singh niranjan
42 Points
8 years ago

first of all we take LCM then it comes ax-ab+bx-ab=x^2+ab-ax-bx

now x^2-2(a+b)x+3ab=0 now roots are equal in magnitude opp. in sign therfoe sum of roots =0

therefor a+b =0

M Ali khan
13 Points
3 years ago
First of all you take LCM then you get
 X^2 -2(a + b)X +3ab = 0
Then apply quadratic formula
  X = -b +- ✓b^2 - 4ac/2a
Then you got 2 answers
 1:  X1 = a + b + ✓a^2 -ab + b^2
 2:  X2 = a + b - ✓a^2 -ab + b^2
  According to the condition
          X1 = -X2
After calculation you got
   a+b = 0
 Hope you understand

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