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Ratio Resolution II (Posted on 2012-11-24) Difficulty: 3 of 5
Each of x, y, z, a, b and c is a positive real number that satisfy:

(ay-bx)/c = (cx-az)/b = (bz-cy)/a

Determine with proof, the ratio x:y:z in terms of a, b and c.

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Hints/Tips re: I think I got it. | Comment 2 of 3 |
(In reply to I think I got it. by Jer)

Nice Proof.

But there is a much simpler solution that covers the more general case where each of a, b and c are any nonzero real numbers. (The specific reason of stating that each of a, b and c is positive is to keep the denominator of  each of the three expressions nonzero.)

HINT

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Assume that  (ay-bx)/c = (cx-az)/b = (bz-cy)/a =p(say)

Then arrive at:

A quadratic expression involving a, b and c multiplied by something is equal to zero and, everything else will just fall in place.

Spoiler Alert:

The quadratic expression and that something are much more simpler than envisaged.  

Edited on November 25, 2012, 3:36 am
  Posted by K Sengupta on 2012-11-25 03:32:28

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