SOLUTION: If log{{x+y}/3}=1/2{logx+log Y}, then find the value of x/y+y/x?

Question 977752: If log{{x+y}/3}=1/2{logx+log Y}, then find the value of x/y+y/x?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
log{{x+y}/3}=1/2{logx+log Y}
log(x+y) - log(3) = 1/2(log xy)
log(xy) - log(2) = 1/2(log xy)
2xy - 4 = xy
xy = 4
now
x/y + y/x =
(x^2 + y^2) / xy =
(x^2 + y^2) / 4
we have two cases
(4, 1) and (2,2) are factors of 4
1) (16 + 1) / 4 = 17/4
2) (4 + 4) / 4 = 2

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