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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: 118

Kudos [?]: 5 [0], given: 0

If x and y are positive, which of following must be greater [#permalink]

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04 Oct 2007, 05:22
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Kudos [?]: 5 [0], given: 0

VP
Joined: 08 Jun 2005
Posts: 1144

Kudos [?]: 246 [0], given: 0

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04 Oct 2007, 06:13
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

Kudos [?]: 246 [0], given: 0

04 Oct 2007, 06:13
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