Anonymous

1/(a+1/(b+1/c))=9/26 9/26= 1/26/9= 1/(2+8/9)= 1/(2+1/(9/8))= 1/(2+1/(1+1/8)) By comparison, a=2 b=1 c=8 => a+b+c=11

Anonymous

I presume a, b & c are positive integers less than 10.

Anonymous

One way to interpret this is “Express 9/26 as a continued fraction” Find the partial quotients: 26/9 = 2 8/9 9/8 = 1 1/8 8/1 = 8 0/8 a = 2 b = 1 c = 8 a+b+c = 11

Anonymous

1 / (a + 1/(b + 1/c)) = 9/26 a + 1/(b + 1/c) = 26/9 9a + 9/(b + 1/c) = 26 a = 2 9 * 2 + 9/(b + 1/c) = 26 18 + 9/(b + 1/c) = 26 9/(b + 1/c) = 8 9 = 8 * (b + 1/c) 9 = 8b + 8/c b = 1 9 = 8 * 1 + 8/c 9 - 8 = 8/c 1 = 8/c c = 8

Anonymous

wow no wonder why you are a failer in school so you can cheat on your math test

Anonymous

Cannot be determined. Here are 3 examples where the expression has value 9/26, but the sum of a, b, and c are all different.

Anonymous

Integer solutions for (a,b,c): (2,1,8) (3,-10,1) (3,-8,-1) (4,-1,10) So the a+b+c = {11 , -8 , -6 , 13} If the question asked for positive integers for a,b,c, then the only answer is 11.