perplexus.info :: Just Math : Real Expression Ratio Resolution

Real Expression Ratio Resolution (Posted on 2016-05-08)

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)

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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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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