perplexus.info :: Just Math : Solution's forecast

Solution's forecast (Posted on 2017-10-24)

Prove that in the set of the equations

(i) x+y+z=a
(ii) 1/x+1/y+1/z=1/a

all possible solutions contain value a as an answer
for one of the uknowns.

Submitted by Ady TZIDON

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Solution: (Hide)

GIVEN :(x+y) = (a-z)
Transform the 2nd equation into (x+y)/xy + 1/z = 1/a.
Substitute for (x+y) and simplify into az(a-z) + xy(a-z) = 0
i.e. ( a-z)(az+xy)= 0 with z=a being a candidate answer.
By symmetry we could get x=a or y=a in the same way.
QED

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
solution	xdog	2017-10-25 12:07:23
re: Sollution	Ady TZIDON	2017-10-25 06:58:01
Sollution	Kenny M	2017-10-24 17:06:56

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