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If a and b are nonzero unequal real numbers and (a−b)/a = b/(a−b), what is the sum of all possible

values for a/b?

 

I had no idea where to start with this one.

 Nov 9, 2022
 #2
avatar+118696 
+3

 

(ab)a=b(ab)(ab)2=aba22ab+b2=aba23ab+b2=0a2+(3b)a+(b2)=0a=3b±9b24b22a=3b±b52

 

a=3b±b52ab=3±52if you add those two possibilities the sum is 6/2=3

 

 

You neeed to check this carefully.

 Nov 9, 2022

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