SOLUTION: If (a-b)^2 - 3(a-b) -18 = 0, find the value of a - b - 8 if a - b - 6 is not equal to 0.

Algebra ->  Rational-functions -> SOLUTION: If (a-b)^2 - 3(a-b) -18 = 0, find the value of a - b - 8 if a - b - 6 is not equal to 0.      Log On


   

Question 1132466: If (a-b)^2 - 3(a-b) -18 = 0, find the value of a - b - 8 if a - b - 6 is not equal to 0.
Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
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If  (a-b)^2 - 3(a-b) -18 = 0.  then


    a-b = use the quadratic formula = %283+%2B-+sqrt%283%5E2+%2B+4%2A18%29%29%2F2 = %283+%2B-+9%29%2F2.


Thus the two roots are


    a-b = %283+%2B+9%29%2F2  = 6 

and

    a-b = %283+-+9%29%2F2 = -3.


Since, according to the condition the value of a-b-6 is not equal to 0, it means that  


    a-b = -3,  and hence  a-b-8 = (a-b+3) - 11 = 0 - 11 = -11.      ANSWER