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Real Expression Ratio Resolution (Posted on 2016-05-08) Difficulty: 3 of 5
Each of X, Y and Z is a distinct nonzero real number such that:
X, Y and Z are in harmonic sequence , and:
X/(Y+Z) = 3/10

Find the possible values of Z/(X+Y)

No Solution Yet Submitted by K Sengupta    
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solution Comment 1 of 1
from their being harmonic, we get
2/y=1/x+1/z
solving x/(y+z)=3/10 for z we get
z=(1/3)*(10x-3y)
substituting into the first equation and solving for y we get
y=4x/3 or y=5x
taking each of these in turn the value
z/(x+y) simplifies to 6/7 and -5/18 respectively

thus the two possible values are 6/7 and -5/18

Edited on May 8, 2016, 9:36 pm
  Posted by Daniel on 2016-05-08 21:34:17

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