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 Silly System (Posted on 2005-05-16)
Solve the system

5^(y-x)*(y+x) = 1
and
(x+y)^(x-y) = 5

 See The Solution Submitted by Jer Rating: 2.7500 (4 votes)

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 Puzzle Solution: Method 2 Comment 6 of 6 |
(In reply to Puzzle Solution: Method 1 by K Sengupta)

Taking logarithm in base 5, we obtain:

log(5)(x+y) = x-y .......(i)
(x-y)*log(5)(x+y) = 1 ....(ii)

Dividing (i) by (ii), we obtain:

1/(x-y) = x-y, so that:
(x-y)^2 = 1, giving:
x-y = +/-1

If x-y = 1, then log(5)(x+y) = 1, so that: x+y = 5
Solving, we have: (x,y) = (3, 2)

If x-y = -1, then log(5)(x+y) = 11, so that: x+y = 1/5
Solving, we have: (x,y) = (-2/5. 3/5).

Consequently, the required solution is given by (x, y) = (3, 2), or (-2/5, 3/5).

 Posted by K Sengupta on 2008-07-03 15:58:06

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