Grade 12Algebra
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?
2 Answers
surendra singh niranjan
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
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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