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If x-2y=4 the minimum value of xy is...

If `x-2y=4` the minimum value of `xy` is

A

`-2`

B

`0`

C

`0`

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `x=-2y=4`
Let `A=xyimpliesA=2y^(2)+4y`
`implies(dA)/(dy)=4y+4`
For maximum or minimum put `(dA)/(dh)=0impliesy=-1`
Now `(d^(2)A)/(dy^(2))=4gt0` minima
At `y=-1, x=4+2(-1)=2`
Then `A=xy=2(-1)=-2`
`:.` Minimum valueof `xy` is `-2`.
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