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If f(x , y) = ((x + y)^2)/(xy) for every...

If `f(x , y) = ((x + y)^2)/(xy)` for every `x, y > 0` then `f(x,y)` must be :

A

`ge 2`

B

`lt 5`

C

`ge 4`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
f9x, y) = `(x^2+y^2+2xy)/(xy) = x/y + y/x +2`
The minimum value of `x/y + y/x` = 2 at x = y
Therefore f(x,y) = `((x+y)/xy)^2 ge 4`
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