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

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Manager
Joined: 13 Jul 2007
Posts: 123
Followers: 2

Kudos [?]: 4 [0], given: 0

If x and y are positive, which of following must be greater [#permalink]  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
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 128 [0], given: 0

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

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