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If x and y are positive, which of following must be greater

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Manager
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Joined: 13 Jul 2007
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If x and y are positive, which of following must be greater [#permalink] New post 04 Oct 2007, 04:22
If x and y are positive, which of following must be greater than 1/(sqrt(x+y))

1. sqrt(x+y)/2x

2. (sqrt(x) + sqrt(y))/(x+y)


3. (sqrt x - sqrt y)/(x+y)

none

1 only

2 only

1 and 3

2 and 3
VP
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 [#permalink] New post 04 Oct 2007, 05:13
1/(sqrt(x+y)) ---> assume x=2 y=2 ---> 1/2

sqrt(x+y)/2x ---> 2/4 = 1/2

(sqrt(x) + sqrt(y))/(x+y) ---> 2.8/4 > 1/2

This is true for every x,y.

since sqrt(x)+sqrt(y) > sqrt(x+y)

(sqrt x - sqrt y)/(x+y) ---> 0

the answer is (C).

:)
  [#permalink] 04 Oct 2007, 05:13
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If x and y are positive, which of following must be greater

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