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)
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)*(10x3y)
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 20160508 21:34:17 