nikhilsrl wrote:

If x and y are positive, which of the following must be greater that 1/sqrt(x + y)?

I. sqrt(x + y)/2x

II. [sqrt(x) + sqrt(y)]/(x + y)

III. [sqrt(x) - sqrt(y)]/(x + y)

a) None

b) I only

c) II only

d) I and II

e) II and III

OA is provided.

Is there an easier to solve this than using numbers.

Looks like "C" to me. Not too sure though.

I. sqrt(x + y)/2x > 1/sqrt(x + y)

x+y > 2x

This is true only for y>x. What if y=x or y<x;

Say; x=2, y=1

3 < 4

Say x=2,y=2

4=4

Proved wrong.

II. [sqrt(x) + sqrt(y)]/(x + y)

[sqrt(x) + sqrt(y)]/(x + y) > 1/sqrt(x+y)

[sqrt(x) + sqrt(y)] > sqrt(x+y)

x=0.25; y=0.25

[sqrt(x) + sqrt(y)] = 0.5+0.5=1

sqrt(x+y) = sqrt(0.25+0.25) = some number between 0 and 1

x=9; y=9

[sqrt(x) + sqrt(y)] = 3+3=6

sqrt(x+y) = sqrt(9+9) = some number between 4 and 5

True.

III. [sqrt(x) - sqrt(y)]/(x + y)

This is simple. x=y; this become 0.

RHS will be some +ve number.

Not true.

Ans: "C"

_________________

~fluke

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